Method and device for determining flow velocity distribution information of target fluid, storage medium and electronic equipment

Abstract

The embodiment of the invention provides a method and device for determining flow velocity distribution information of target fluid, a storage medium and electronic equipment, and the method comprises the steps: constructing a Poiseuille flow equation according to fluid parameters of the target fluid; converting the Poiseuille flow equation into linear systems on different sub-domains through a finite difference algorithm and a region decomposition algorithm to obtain a plurality of linear systems; the first linear system is solved through a probability calculation algorithm to obtain a first sub-domain solution, the second linear system is solved through a classical algorithm to obtain a second sub-domain solution, the multiple linear systems comprise the first linear system and the second linear system, the performance requirement of the first linear system is higher than or equal to a preset threshold value, and the performance requirement of the second linear system is higher than or equal to the preset threshold value. The performance requirement of the second linear system is lower than the preset threshold value, and the performance requirements of the multiple linear systems are determined according to sub-domain parameters of different sub-domains; and determining a target solution of the Poiseuille flow equation according to the first sub-domain solution and the second sub-domain solution.

Description

Technical Field

[0001] The embodiments of the present application relate to the field of computers, and more specifically, to a method and device for determining flow velocity distribution information of a target fluid, a storage medium, and an electronic device. Background Art

[0002] Solving the Poiseuille flow equation usually requires highly complex numerical calculation methods, which have extremely large demands on computing resources when dealing with large-scale, high-precision flow problems. For example, in order to obtain the precise flow distribution of fluids in complex geometric structures, calculations need to be performed on extremely fine grids, which often leads to huge consumption of supercomputing power. Currently, classical computers face severe performance challenges when dealing with such large-scale, high-precision computing tasks. Problems such as long calculation time, high energy consumption, and large resource usage limit the popularity and efficiency of the Poiseuille flow model in practical engineering applications.

[0003] Regarding the related technologies, the current method for solving the Poiseuille flow equation requires enormous supercomputing power, which poses a severe challenge to the performance of current classical computers, and no effective solution has yet been proposed. Summary of the invention

[0004] The embodiments of the present application provide a method and device for determining the flow velocity distribution information of a target fluid, a storage medium, and an electronic device, so as to at least solve the problem in the related art that the current method for solving the Poiseuille flow equation requires huge supercomputing power, posing a severe challenge to the performance of current classical computers.

[0005] According to one embodiment of the present application, a method for determining flow velocity distribution information of a target fluid is provided, comprising: constructing a Poiseuille flow equation according to fluid parameters of the target fluid, wherein the Poiseuille flow equation is used to determine the flow velocity distribution information of the target fluid; converting the Poiseuille flow equation into linear systems on different subdomains by a finite difference algorithm and a domain decomposition algorithm to obtain a plurality of linear systems; solving a first linear system by a probability calculation algorithm to obtain a first subdomain solution, and solving a second linear system by a classical algorithm to obtain a second subdomain solution, wherein the plurality of linear systems include the first linear system and the second linear system, the performance requirement of the first linear system is higher than or equal to a preset threshold, the performance requirement of the second linear system is lower than the preset threshold, and the performance requirements of the plurality of linear systems are determined according to the subdomain parameters of the different subdomains; determining a target solution of the Poiseuille flow equation according to the first subdomain solution and the second subdomain solution, wherein the target solution is used to indicate the flow velocity distribution information of the target fluid.

[0006] In an exemplary embodiment, the Poiseuille flow equation is converted into linear systems on different subdomains by a finite difference algorithm and a regional decomposition algorithm to obtain a plurality of linear systems, including: discretizing the Poiseuille flow equation by the finite difference algorithm to obtain a target linear system, and acquiring parameter information of the target linear system; decomposing the domain of the Poiseuille flow equation by the regional decomposition algorithm to obtain a plurality of subdomains; and discretizing the Poiseuille flow equation by the finite difference algorithm in the plurality of subdomains according to the parameter information to obtain the plurality of linear systems.

[0007] In an exemplary embodiment, the Poiseuille flow equation is , x, y represent the liquid flow direction and longitudinal coordinate respectively, represents the flow velocity in the x direction, represents the fluid density, express The pressure gradient in the direction, represents the viscosity of the fluid, represents time, the boundary condition of the Poiseuille flow equation is: when hour, , h represents the distance between the parallel plate and the center line of the two parallel plates, the finite difference algorithm is used to discretize the Poiseuille flow equation to obtain the target linear system, including: dividing the interval (-h, h) into n+1 parts along the y direction to obtain n+1 sub-intervals, and dividing the time t into T parts to obtain T discretized times, wherein the interval interval of each sub-interval is , the discretization time step size for each discretization time ; Use the preset finite difference format to approximate the first and second order derivatives to obtain: , where the superscript + indicates that the velocity at the next time step is unknown, and the subscript , , Respectively indicate along Three adjacent points obtained after direction discretization; apply all discretized points along the y direction to the formula The target linear system is obtained from ,in, matrix, For one dimensional vector, , , , .

[0008] In an exemplary embodiment, the domain of the Poiseuille flow equation is decomposed by the regional decomposition algorithm to obtain multiple subdomains, including: decomposing the domain into the multiple subdomains by the regional decomposition algorithm, wherein the boundaries of two adjacent subdomains in the multiple subdomains overlap; determining the value ranges of the multiple subdomains, wherein the value ranges include: the coordinate range of the subdomain in the flow direction, and the coordinate range perpendicular to the flow direction; determining the boundary conditions adopted by the Poiseuille flow equation in each subdomain, wherein the boundary conditions include: the restriction conditions of the fluid velocity at the subdomain boundaries.

[0009] In an exemplary embodiment, the Poiseuille flow equation is discretized by the finite difference algorithm in the multiple subdomains to obtain the multiple linear systems, including: in each subdomain, discretizing the domain of the subdomain into multiple discrete points; performing differential operations on the function values ​​of the Poiseuille flow equation at the multiple discrete points to obtain multiple finite difference expressions; at each discrete point, replacing the derivative of the Poiseuille flow equation with the corresponding finite difference expression to obtain the discretized equation at the discrete point; and combining the discretized equations at the multiple discrete points to obtain a linear system.

[0010] In an exemplary embodiment, before solving the first linear system by a probability calculation algorithm to obtain a first subdomain solution, and solving the second linear system by a classical algorithm to obtain a second subdomain solution, the method further includes: performing parameter analysis on the multiple subdomains to obtain subdomain parameters of the multiple subdomains, and performing parameter analysis on the multiple linear systems to obtain system parameters of the multiple linear systems; performing performance requirement evaluation on the multiple linear systems based on the subdomain parameters and the system parameters to obtain performance requirements of the multiple linear systems; and classifying the multiple linear systems into the first linear system and the second linear system based on the multiple performance requirements and the preset threshold.

[0011] In an exemplary embodiment, solving the first linear system by a probability calculation algorithm to obtain a first subdomain solution includes: designing the probability calculation algorithm for the first linear system; running the probability calculation algorithm to obtain a binary representation of the first subdomain solution; reading the binary representation of the first subdomain solution, and converting the binary representation of the first subdomain solution back into a solution vector of the first linear system to obtain the first subdomain solution.

[0012] In an exemplary embodiment, the probability calculation algorithm is designed for the first linear system, including: constructing a target loss function for solving the first linear system, wherein the minimum value of the target loss function corresponds to the optimal solution of the first linear system; converting the solution vector of the first linear system into binary form to represent multiple elements in the solution vector by a preset number of probability bits; taking partial derivatives of the multiple elements through the target loss function to determine the input signal of the probability calculation algorithm and the update rule of the solution vector; determining the probability calculation algorithm according to the target loss function, the binary solution vector, the input signal and the update rule.

[0013] In an exemplary embodiment, the objective loss function includes: = ,in, is the coefficient matrix of the first linear system, is the bias vector of the first linear system, the vector is the solution vector of the first linear system, the vector is a vector The conjugate transpose of .

[0014] In an exemplary embodiment, solving the second linear system by a classical algorithm to obtain a second subdomain solution includes: running the classical algorithm to obtain the second subdomain solution, wherein the classical algorithm includes one of the following: a chase method, a Gaussian elimination method.

[0015] In an exemplary embodiment, determining the target solution of the Poiseuille flow equation based on the first subdomain solution and the second subdomain solution includes: performing a boundary continuity check on the first subdomain solution and the second subdomain solution, and adjusting the boundary values ​​of the first subdomain solution and the second subdomain solution according to the check result to obtain an adjusted first subdomain solution and an adjusted second subdomain solution; and sequentially splicing the adjusted first subdomain solution and the adjusted second subdomain solution in the order of multiple subdomains to obtain the target solution.

[0016] According to another embodiment of the present application, a device for determining flow velocity distribution information of a target fluid is provided, comprising: a construction module, configured to construct a Poiseuille flow equation according to fluid parameters of the target fluid, wherein the Poiseuille flow equation is used to determine the flow velocity distribution information of the target fluid; a conversion module, configured to convert the Poiseuille flow equation into linear systems on different subdomains through a finite difference algorithm and a domain decomposition algorithm to obtain a plurality of linear systems; a solution module, configured to solve a first linear system through a probability calculation algorithm to obtain a first subdomain solution, and to solve a second linear system through a classical algorithm to obtain a second subdomain solution, wherein the plurality of linear systems include the first linear system and the second linear system, the performance requirement of the first linear system is higher than or equal to a preset threshold, the performance requirement of the second linear system is lower than the preset threshold, and the performance requirements of the plurality of linear systems are determined according to the subdomain parameters of the different subdomains; a determination module, configured to determine a target solution of the Poiseuille flow equation according to the first subdomain solution and the second subdomain solution, wherein the target solution is used to indicate the flow velocity distribution information of the target fluid.

[0017] According to another embodiment of the present application, a computer-readable storage medium is provided, in which a computer program is stored, wherein the computer program is configured to execute the steps of any of the above method embodiments when run.

[0018] According to another embodiment of the present application, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor is configured to run the computer program to execute the steps in any one of the above method embodiments.

[0019] According to another embodiment of the present application, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps of the method described in each embodiment of the present application are implemented.

[0020] According to the present application, a Poiseuille flow equation is first constructed according to the fluid parameters of the target fluid, so as to determine the flow velocity distribution information of the target fluid through the Poiseuille flow equation; then, the Poiseuille flow equation is converted into a linear system on different subdomains through a finite difference algorithm and a regional decomposition algorithm to obtain a plurality of linear systems; then, the first linear system is solved through a probability calculation algorithm to obtain a first subdomain solution, and the second linear system is solved through a classical algorithm to obtain a second subdomain solution, wherein the plurality of linear systems include a first linear system and a second linear system, the performance requirement of the first linear system is higher than or equal to a preset threshold, and the performance requirement of the second linear system is lower than the preset threshold, and the performance requirements of these linear systems are based on the subdomains of different subdomains. The parameters are determined; finally, the target solution of the Poiseuille flow equation is determined according to the first subdomain solution and the second subdomain solution, the Poiseuille flow equation is solved, and the flow velocity distribution information of the target fluid is determined; the above scheme is adopted to solve the linear system design corresponding to the high performance requirement, and the linear system involving low performance requirement is solved by the classical algorithm, and the performance advantage of probability calculation and the outstanding performance of classical computers in processing traditional complex computing problems are used to solve the Poiseuille flow problem, so as to improve the efficiency of solving complex problems and reduce the required supercomputing power; thereby solving the problem in the related technology that the current solution method of the Poiseuille flow equation requires huge supercomputing power, which poses a severe challenge to the performance of current classical computers. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a hardware structure block diagram of a computer terminal of a method for determining flow velocity distribution information of a target fluid according to an embodiment of the present application;

[0022] Figure 2 is a schematic diagram of an optional two-dimensional incompressible Poiseuille flow according to an embodiment of the present application;

[0023] Figure 3 is a flow chart of an optional method for determining flow velocity distribution information of a target fluid according to an embodiment of the present application;

[0024] Figure 4 is a schematic diagram of an optional solution process of a Poiseuille flow problem according to an embodiment of the present application;

[0025] Figure 5 It is a structural block diagram of an optional device for determining flow velocity distribution information of a target fluid according to an embodiment of the present application. DETAILED DESCRIPTION

[0026] The embodiments of the present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0027] It should be noted that the terms "first", "second", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

[0028] The method embodiments provided in the embodiments of the present application can be executed in a computer terminal or a similar computing device. Taking running on a computer terminal as an example, Figure 1 1 is a hardware structure block diagram of a computer terminal for determining flow velocity distribution information of a target fluid according to an embodiment of the present application. Figure 1 As shown, the computer terminal may include one or more ( Figure 1 Only one is shown in the figure) a processor 102 (the processor 102 may include but is not limited to a processing device such as a microprocessor MCU or a programmable logic device FPGA) and a memory 104 for storing data, wherein the above-mentioned computer terminal may also include a transmission device 106 and an input and output device 108 for communication functions. It can be understood by those skilled in the art that Figure 1 The structure shown is only for illustration and does not limit the structure of the above-mentioned computer terminal. Figure 1 More or fewer components as shown, or with Figure 1 Different configurations shown.

[0029] The memory 104 can be used to store computer programs, for example, software programs and modules of application software, such as the computer program corresponding to the method for determining the flow velocity distribution information of the target fluid in the embodiment of the present application. The processor 102 executes various functional applications and data processing by running the computer program stored in the memory 104, that is, to implement the above method. The memory 104 may include a high-speed random access memory, and may also include a non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some examples, the memory 104 may further include a memory remotely arranged relative to the processor 102, and these remote memories may be connected to the computer terminal via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0030] The transmission device 106 is used to receive or send data via a network. The specific example of the above network may include a wireless network provided by a communication provider of a computer terminal. In one example, the transmission device 106 includes a network adapter (Network Interface Controller, referred to as NIC), which can be connected to other network devices through a base station so as to communicate with the Internet. In one example, the transmission device 106 can be a radio frequency (RF) module, which is used to communicate with the Internet wirelessly.

[0031] The following is an explanation of the professional terms that appear in this application:

[0032] p-bit: probabilistic bit, which randomly represents 0 and 1 with a certain probability within a certain period of time.

[0033] It should be noted that the probabilistic bit (p-bit) is different from the classical bit (bit). Its state is to randomly represent 0 or 1 with a certain probability within a certain period of time. It is a basic unit for probabilistic computers to process information. Specifically, a single probabilistic bit can use the random "up" and "down" states of spin particles to represent 0 and 1 in binary operations, and the probability of each state is 50%. By utilizing the complex correlations of coupling and mutual influence between multiple probabilistic bits, probabilistic computers can be constructed to effectively solve optimization problems.

[0034] It should be noted that Poiseuille flow refers to the laminar flow on an infinitely long straight circular tube. In the case of two-dimensional incompressibility, it specifically refers to the two-dimensional, steady, incompressible flow between two parallel plates, and there is only a flow velocity in a certain direction (such as the x direction). The two-dimensional incompressible Poiseuille flow can be described by the following equation: ,in, , represent the liquid flow direction and the longitudinal coordinate respectively, express The flow velocity in the direction, represents the fluid density, express The pressure gradient in the direction, represents the viscosity of the fluid, represents time. The boundary condition is when hour, ,in represents the distance between the parallel plate and the center line of the two parallel plates, as shown in Figure 2 shown.

[0035] The velocity distribution of two-dimensional incompressible Poiseuille flow reveals the flow characteristics of fluid between parallel plates. The velocity is small near the plate, while the velocity reaches its maximum value at the center between the plates. This flow characteristic is of great significance for understanding the flow behavior of fluids in pipes or between plates. Poiseuille flow has a wide range of applications in microfluidic chips, biomedical engineering, chemical engineering and other fields. For example, in microfluidic chips, precise control and separation of microparticles can be achieved by precisely controlling the velocity distribution of Poiseuille flow; in biomedical engineering, Poiseuille flow is used to simulate the flow of blood in blood vessels to study the occurrence and development mechanism of vascular diseases.

[0036] In this embodiment, a method for determining flow velocity distribution information of a target fluid is provided. Figure 3 is a flow chart of a method for determining flow velocity distribution information of a target fluid according to an embodiment of the present application. Figure 3 As shown, the method comprises the following steps:

[0037] Step S304, constructing a Poiseuille flow equation according to the fluid parameters of the target fluid, wherein the Poiseuille flow equation is used to determine the flow velocity distribution information of the target fluid;

[0038] Step S304, converting the Poiseuille flow equation into linear systems on different subdomains by using a finite difference algorithm and a domain decomposition algorithm to obtain multiple linear systems;

[0039] Step S306, solving the first linear system by a probability calculation algorithm to obtain a first subdomain solution, and solving the second linear system by a classical algorithm to obtain a second subdomain solution, wherein the multiple linear systems include the first linear system and the second linear system, the performance requirement of the first linear system is higher than or equal to a preset threshold, the performance requirement of the second linear system is lower than the preset threshold, and the performance requirements of the multiple linear systems are determined according to the subdomain parameters of the different subdomains;

[0040] Step S308: determining a target solution of the Poiseuille flow equation according to the first subdomain solution and the second subdomain solution, wherein the target solution is used to indicate flow velocity distribution information of the target fluid.

[0041] Through the above scheme, a Poiseuille flow equation is first constructed according to the fluid parameters of the target fluid, so as to determine the flow velocity distribution information of the target fluid through the Poiseuille flow equation; then, the Poiseuille flow equation is converted into a linear system on different subdomains through a finite difference algorithm and a regional decomposition algorithm to obtain a plurality of linear systems; then, the first linear system is solved through a probability calculation algorithm to obtain a first subdomain solution, and the second linear system is solved through a classical algorithm to obtain a second subdomain solution, wherein the plurality of linear systems include a first linear system and a second linear system, the performance requirement of the first linear system is higher than or equal to a preset threshold, and the performance requirement of the second linear system is lower than the preset threshold, and the performance requirements of these linear systems are based on the subdomains of different subdomains. The parameters are determined; finally, the target solution of the Poiseuille flow equation is determined according to the first subdomain solution and the second subdomain solution, the Poiseuille flow equation is solved, and the flow velocity distribution information of the target fluid is determined; the above scheme is adopted to solve the linear system design corresponding to the high performance requirement, and the linear system involving low performance requirement is solved by the classical algorithm, and the performance advantage of probability calculation and the outstanding performance of classical computers in processing traditional complex computing problems are used to solve the Poiseuille flow problem, so as to improve the efficiency of solving complex problems and reduce the required supercomputing power; thereby solving the problem in the related technology that the current solution method of the Poiseuille flow equation requires huge supercomputing power, which poses a severe challenge to the performance of current classical computers.

[0042] In an exemplary embodiment, the Poiseuille flow equation is converted into linear systems on different subdomains by a finite difference algorithm and a regional decomposition algorithm to obtain a plurality of linear systems, including: discretizing the Poiseuille flow equation by the finite difference algorithm to obtain a target linear system, and acquiring parameter information of the target linear system; decomposing the domain of the Poiseuille flow equation by the regional decomposition algorithm to obtain a plurality of subdomains; and discretizing the Poiseuille flow equation by the finite difference algorithm in the plurality of subdomains according to the parameter information to obtain the plurality of linear systems.

[0043] This embodiment describes the specific implementation steps of converting the Poiseuille flow equation into a linear system problem on multiple subdomains using a finite difference algorithm and a domain decomposition algorithm. The following is a detailed description of this process:

[0044] 1. Finite difference algorithm discretization processing:

[0045] 1) Overall discretization: First, the entire Poiseuille flow equation (i.e., the equation describing the steady flow of fluid between parallel plates) is discretized using the finite difference algorithm. This involves converting the continuous equation into a series of algebraic equations at discrete grid points. Specifically, the space and time within the domain are divided into several small grids, and the fluid properties (such as flow velocity) on each grid are approximated by the values ​​at the grid points.

[0046] 2) Generate target linear system: After the finite difference algorithm is used, the Poiseuille flow equation is transformed into a target linear system in the form of , where A is the coefficient matrix, x is the unknown vector, and b is the known vector. This linear system contains equations and boundary conditions at all discrete grid points and is the mathematical expression of the problem to be solved.

[0047] 2. Domain Decomposition Algorithm Definition Domain Decomposition:

[0048] 1) Subdomain division: Then, the domain of the Poiseuille flow equation is divided into multiple subdomains using the regional decomposition algorithm. These subdomains can be overlapping or non-overlapping, and the basis for division can be the geometric characteristics of the domain, the physical characteristics of the flow, and the accuracy requirements of the desired calculation.

[0049] 2) Determine subdomain characteristics: For each subdomain, determine its spatial value range, boundary conditions, and internal grid density. Boundary conditions are the fluid property values ​​or change rates at the interfaces between the subdomain and the entire definition domain and adjacent subdomains.

[0050] 3. Discretization processing within the subdomain:

[0051] 1) Subdomain discretization: The finite difference algorithm is applied again in each subdomain to discretize the Poiseuille flow equation. This means that the Poiseuille flow equation in each subdomain is also transformed into an independent linear system problem, and the linear system of each subdomain reflects the flow characteristics in the region.

[0052] 2) Obtaining sublinear systems: By applying the finite difference algorithm in the subdomain, multiple independent linear system equations can be obtained, each corresponding to the fluid flow in a subdomain. These sublinear systems are part of the target linear system, but they are solved independently.

[0053] Through the above steps, the original Poiseuille flow equation is transformed and decomposed into a target linear system, which is further divided into multiple sub-linear systems, each of which corresponds to a subdomain in the definition domain. This method allows us to adopt different solution strategies (such as probabilistic calculation and classical calculation) for the characteristics of different subdomains (such as mesh density and flow complexity), thereby improving the overall solution efficiency and reducing the consumption of computing resources, while ensuring that the accuracy of the solution meets actual needs. Finally, through data fusion or subdomain solution merging technology, the solutions of all subdomains are integrated into a global solution, thus completing the solution process of the entire Poiseuille flow problem.

[0054] Furthermore, the Poiseuille flow equation is: , x, y represent the liquid flow direction and longitudinal coordinate respectively, represents the flow velocity in the x direction, represents the fluid density, express The pressure gradient in the direction, represents the viscosity of the fluid, represents time, the boundary condition of the Poiseuille flow equation is: when hour, , h represents the distance between the parallel plate and the center line of the two parallel plates, the finite difference algorithm is used to discretize the Poiseuille flow equation to obtain the target linear system, including: dividing the interval (-h, h) into n+1 parts along the y direction to obtain n+1 sub-intervals, and dividing the time t into T parts to obtain T discretized times, wherein the interval interval of each sub-interval is , the discretization time step size for each discretization time ; Use the preset finite difference format to approximate the first and second order derivatives to obtain: , where the superscript + indicates that the velocity at the next time step is unknown, and the subscript , , Respectively indicate along Three adjacent points obtained after direction discretization; apply all discretized points along the y direction to the formula The target linear system is obtained from ,in, matrix, For one dimensional vector, , , , .

[0055] This embodiment describes in detail the process of discretizing the Poiseuille flow equation through the finite difference algorithm and then converting it into a linear system problem. Below, we analyze the steps of this embodiment one by one:

[0056] First, the Poiseuille flow equation describes the characteristics of fluid flow in an infinitely long straight circular tube or between two parallel plates. The equation is expressed as:

[0057] ,

[0058] Where: x, y represent the liquid flow direction and longitudinal coordinate respectively, represents the flow velocity in the x direction, represents the fluid density, express The pressure gradient in the direction, represents the viscosity of the fluid, The domain of time y is ((-h, h)), where (h) is the distance between the parallel plates and the centerline of the two parallel plates.

[0059] 1. Discretization processing:

[0060] Time and space discretization: The interval ((-h, h)) of the vertical coordinate (y) is evenly divided into (n+1) subintervals, and the interval of each subinterval is (△y). At the same time, the time (t) is evenly divided into (T) parts, and the length of each discretization time step is This step transforms continuous space and time into a series of discrete points, providing a basis for the establishment of subsequent discrete equations.

[0061] 2. Formula difference approximation: Use the finite difference format to approximate the first and second order derivatives in the Poiseuille flow equation. For example, for the second order derivative in the (y) direction, the central difference formula can be expressed as:

[0062] , where the superscript + indicates that the velocity at the next time step is unknown; the subscript , , Respectively indicate along Three adjacent points obtained after direction discretization.

[0063] 3. Construct a linear system: Apply all discretized points to the finite difference approximation formula to obtain a series of algebraic equations, and then construct the target linear system. The form of this linear system is:

[0064] , for a steady flow (the flow does not change with time), we have , so the linear system becomes ,in, matrix, For one dimensional vector, , , , , according to the specific application scenario , , , , The assignment obtains the specific expression of the above linear system.

[0065] Through the above steps, the Poiseuille flow equation is transformed into a linear system problem, which is the basis for further processing by the probabilistic-classical hybrid solver. Subsequently, through the domain decomposition algorithm, this linear system can be further decomposed into various subdomains, and the optimal solution strategy can be designed for each subdomain, thereby allocating computing tasks between probabilistic computers and classical computers to achieve efficient collaborative solution.

[0066] Furthermore, the domain of the Poiseuille flow equation is decomposed by the regional decomposition algorithm to obtain multiple subdomains, including: decomposing the domain into the multiple subdomains by the regional decomposition algorithm, wherein the boundaries of two adjacent subdomains in the multiple subdomains overlap; determining the value ranges of the multiple subdomains, wherein the value ranges include: the coordinate range of the subdomain in the flow direction, and the coordinate range perpendicular to the flow direction; determining the boundary conditions adopted by the Poiseuille flow equation in each subdomain, wherein the boundary conditions include: the restriction conditions of the fluid velocity at the subdomain boundaries.

[0067] This embodiment describes how to use the regional decomposition algorithm to decompose the definition domain of the Poiseuille flow equation into multiple subdomains, and determine the appropriate value range and boundary conditions for each subdomain, so as to solve the problem more efficiently. The following is a detailed analysis:

[0068] 1. Domain decomposition: The domain decomposition algorithm first divides the entire domain of the Poiseuille flow equation (i.e., the region where the fluid flow occurs, for Poiseuille flow, it is the region between an infinitely long straight circular tube or two parallel plates) into multiple subdomains. These subdomains can be continuous or overlapping. In particular, the boundaries of adjacent subdomains may overlap. The purpose of the overlap is to ensure the continuity of the solution and the uniformity of the boundary conditions when merging the subdomain solutions.

[0069] 2. Determine the subdomain value range: For each subdomain, it is necessary to clarify its coordinate range in the flow direction (x direction) and the vertical flow direction (y direction).

[0070] 3. Boundary conditions: The Poiseuille flow equation on each subdomain needs to be solved according to its boundary conditions. Boundary conditions include restrictions on the fluid velocity at the subdomain boundary. For example, at the parallel plate boundary, the fluid velocity is usually zero; while at the internal boundary of the subdomain (the overlapping area with the adjacent subdomain), the boundary conditions may be set according to the fluid velocity of the adjacent subdomain to ensure continuous flow and matching of the fluid velocity.

[0071] By implementing the above steps, it is possible to ensure that the Poiseuille flow equation has clear boundary conditions and value ranges in each subdomain, which provides a basis for solving linear system problems in different subdomains on probabilistic computers and classical computers respectively. Finally, by merging the solutions of all subdomains, the numerical solution of the Poiseuille flow equation on the entire definition domain can be obtained, achieving efficient solution of complex problems. This method is particularly useful when dealing with large-scale problems because it allows parallel computing and can use probabilistic computing techniques in subdomains with higher performance requirements and classical computing techniques in subdomains with lower performance requirements, thereby saving resources and improving computing power.

[0072] Optionally, the Poiseuille flow equation is discretized by the finite difference algorithm in the multiple subdomains to obtain the multiple linear systems, including: in each subdomain, discretizing the definition domain of the subdomain into multiple discrete points; performing differential operations on the function values ​​of the Poiseuille flow equation at the multiple discrete points to obtain multiple finite difference expressions; at each discrete point, replacing the derivative of the Poiseuille flow equation with the corresponding finite difference expression to obtain the discretized equation at the discrete point; and combining the discretized equations at the multiple discrete points to obtain a linear system.

[0073] This embodiment describes in detail how to discretize the Poiseuille flow equation in multiple subdomains of the Poiseuille flow problem by using a finite difference algorithm to generate multiple linear systems, which facilitates the subsequent use of different calculation strategies in different subdomains for solving. The following is a specific description:

[0074] 1. Discretization of subdomain definition domain: In each subdomain, first, discretize the subdomain definition domain into a series of discrete points along the x and y directions. This usually means dividing the spatial coordinate axis into a series of evenly spaced points that form a grid structure, and the flow velocity and pressure at each point can be calculated independently.

[0075] 2. Difference operation: At each discrete point, the function value of the Poiseuille flow equation is approximated by the finite difference of the first and second order derivatives. The finite difference expression estimates the derivative of the Poiseuille flow equation at that point by using the function value of the surrounding discrete points. For example, the first order derivative can be expressed using forward or backward difference, while the second order derivative is usually expressed using central difference.

[0076] 3. Discretization equation: At each discrete point, replace the derivative term in the Poiseuille flow equation with its corresponding finite difference expression to generate the discretization equation at the discrete point. This step converts the original differential equation into a series of algebraic equations, each corresponding to a discrete point.

[0077] 4. Linear system construction: Combine the discretized equations at all discrete points to form a linear system. This linear system can be described as , where A is the coefficient matrix, x is a vector containing the unknown flow velocities at all discrete points, and b is a vector consisting of boundary conditions and known physical parameters.

[0078] Through this process, the Poiseuille flow equation in each subdomain is transformed into an independent linear system problem, which can be solved on the probabilistic and classical computing platforms respectively, thereby making full use of their respective advantages and improving the overall solution efficiency of the Poiseuille flow problem. Finally, by merging the solutions of all subdomains, the numerical solution of the entire Poiseuille flow equation can be obtained.

[0079] Optionally, before solving the first linear system by a probability calculation algorithm to obtain a first subdomain solution, and solving the second linear system by a classical algorithm to obtain a second subdomain solution, the method further includes: performing parameter analysis on the multiple subdomains to obtain subdomain parameters of the multiple subdomains, and performing parameter analysis on the multiple linear systems to obtain system parameters of the multiple linear systems, wherein the subdomain parameters include: subdomain flow characteristics, complexity of the boundary conditions, and the system parameters include: scale of the linear system, condition number of the linear system; performing performance requirement evaluation on the multiple linear systems according to the subdomain parameters and the system parameters to obtain performance requirements of the multiple linear systems; and classifying the multiple linear systems into the first linear system and the second linear system according to the multiple performance requirements and the preset threshold.

[0080] Before using the probability calculation algorithm and the classical algorithm to solve the linear systems in multiple subdomains of the Poiseuille flow problem, this embodiment emphasizes a key preprocessing step - parameter analysis, which is to better determine which linear systems on subdomains are suitable for solving with probability calculation and which are more suitable for classical calculation. Parameter analysis helps us identify the characteristics of different subdomains and the properties of their corresponding linear systems, so as to reasonably allocate computing resources. The following is a detailed description of this embodiment:

[0081] 1. Subdomain parameter analysis: Before starting the solution, first perform parameter analysis on each subdomain, which includes but is not limited to examining the flow characteristics within the subdomain, the complexity of the boundary conditions, etc. The flow characteristics may involve the magnitude of the flow velocity, the stability of the flow, etc., while the complexity of the boundary conditions reflects the nonlinearity of the boundary conditions, the complexity of the boundary shape, etc. These parameters will help us understand the flow behavior within each subdomain and the difficulty of solving the problem.

[0082] 2. Linear system parameter analysis: Next, perform parameter analysis on the linear system of each subdomain obtained by discretization, focusing on the size of the linear system (that is, the number of unknowns) and the condition number of the linear system (reflecting the numerical stability of the matrix). The larger the condition number, the more unstable the system is and the more difficult it is to solve. Large-scale systems may require more computing resources and time.

[0083] For example, if the number of grid points in a subdomain is very large and the boundary conditions involve complex nonlinear functions, the linear system in this subdomain may be large in scale and the condition number may also be large, which means that it has high requirements for computational accuracy and resources.

[0084] 3. Determine the category of performance requirements: Based on the above analysis, the category of performance requirements for solving linear systems on each subdomain can be determined. Generally, we classify linear systems with large scale, complex boundary conditions and high condition numbers as having high performance requirements, while systems with smaller scale, simple boundary conditions and lower condition numbers are classified as having low performance requirements.

[0085] For example, subdomain 1 may be identified as having high performance requirements due to its high flow rate and high mesh density; while subdomain 2 may be identified as having low performance requirements due to its stable flow rate and low mesh density.

[0086] 4. Linear system classification: Finally, according to the performance requirement category of each linear system, they are classified into first linear systems (high performance requirements) and second linear systems (low performance requirements). This will guide us to adopt different computing strategies for solving: the first linear system is suitable for the use of probabilistic computing algorithms because it can handle large-scale and complex problems and may show advantages in computing efficiency and resource consumption; while the second linear system is more suitable for the use of classical algorithms, such as Gaussian elimination method, conjugate gradient method, etc. These methods usually perform better when dealing with smaller-scale linear systems with better numerical stability.

[0087] For example, in the context of Poiseuille flow problems, the linear system on subdomain 1 may be classified as a first linear system and solved by a probabilistic algorithm, while the linear system on subdomain 2 may be classified as a second linear system and solved by a classical algorithm.

[0088] Through this systematic classification based on parameter analysis, we can more effectively distribute tasks between probabilistic and classical computers, give full play to the advantages of each, and reduce the overall computing cost and improve the efficiency of solving problems. This approach is particularly suitable for scientific computing fields that require processing large amounts of data and complex calculations, such as fluid dynamics, where the computing requirements of different parts may vary greatly.

[0089] Optionally, solving the first linear system by using a probability calculation algorithm to obtain a first subdomain solution includes: designing the probability calculation algorithm for the first linear system; running the probability calculation algorithm to obtain a binary representation of the first subdomain solution; reading the binary representation of the first subdomain solution, and converting the binary representation of the first subdomain solution back into a solution vector of the first linear system to obtain the first subdomain solution.

[0090] This embodiment describes how to use the probability calculation algorithm to solve the first linear system (i.e., the subdomain linear system with high requirements for computing performance) divided from the Poiseuille flow problem, and finally obtain the solution of the subdomain. The following is a detailed description of the specific steps:

[0091] 1. Design a probability calculation algorithm: First, design a special probability calculation algorithm for the first linear system. This includes constructing an objective loss function whose minimization is directly related to the solution of the first linear system.

[0092] 2. Run the probability calculation algorithm: Input the designed probability calculation algorithm into the probability computer for operation. The probability computer uses the probability bit as the basic calculation unit, and its state switches randomly between 0 and 1 with a certain probability. By simulating the evolution process of physical systems (such as spin systems), the probability computer can solve complex optimization problems. When running the probability calculation algorithm, the probability computer will output the binary representation of x, which is obtained through multiple random sampling and optimization iterations, reflecting the most likely solution vector state.

[0093] For example, if the solution vector x of the first linear system is a vector containing 16 elements, the probabilistic computer will output a 16-bit string, with each bit representing the binary value of the solution vector element at the corresponding position. This process may involve complex probabilistic state evolution and optimization to find the binary representation of the solution vector that minimizes the target loss function.

[0094] 3. Read and convert the solution vector: After reading the binary representation of the first subdomain solution from the probability computer, it needs to be converted back to the solution vector format of the first linear system. This usually involves decoding the binary bit string into the actual numerical solution. For example, if each element of the solution vector uses a 2-bit binary representation, the 16-element binary bit string needs to be converted into a 16-dimensional real vector.

[0095] Through the above steps, we can effectively use the characteristics of probabilistic computing to process the first linear system in the complex and high-precision Poiseuille flow problem, thereby obtaining the first subdomain solution, which provides a key solution for the subsequent subdomain solution fusion and the solution of the entire Poiseuille flow problem. This method fully utilizes the advantages of probabilistic computing in dealing with large-scale optimization problems, while avoiding the bottlenecks and inefficiencies that classical computing may encounter when dealing with such complex problems.

[0096] Optionally, designing the probability calculation algorithm for the first linear system includes: constructing a target loss function for solving the first linear system, wherein the minimum value of the target loss function corresponds to the optimal solution of the first linear system; converting the solution vector of the first linear system into binary form to represent multiple elements in the solution vector by a preset number of probability bits; taking partial derivatives of the multiple elements through the target loss function to determine the input signal of the probability calculation algorithm and the update rule of the solution vector; determining the probability calculation algorithm according to the target loss function, the binary solution vector, the input signal and the update rule.

[0097] Optionally, the objective loss function includes: = ,in, is the coefficient matrix of the first linear system, is the bias vector of the first linear system, the vector is the solution vector of the first linear system, the vector is a vector The conjugate transpose of .

[0098] This embodiment describes in depth the process of designing a probability calculation algorithm to solve the first linear system with high performance requirements in the Poiseuille flow problem. The following is a description of the detailed steps:

[0099] 1. Construct the target loss function: The core of probability calculation is to find the solution to the problem by optimizing the target function. , the objective function is usually designed as a function related to the system error, which may be in the form of = ,in is the coefficient matrix of the first linear system, is the bias vector of the first linear system, the vector is the solution vector of the first linear system, the vector is a vector The conjugate transpose of . The minimum value of the objective function should correspond to the optimal solution vector of the first linear system. This function design ensures that the optimization process is directly related to the solution of the linear system, so that the algorithm is also approaching the solution of the linear system when searching for the minimum value.

[0100] 2. Binary conversion of solution vector: In order to run on a probabilistic computer, the solution vector of the first linear system needs to be converted into binary form. Each element (x_i) of the solution vector is represented by a certain number of bits, which is called probability bits (p-bits). For example, if each element (x_i) is represented by a 4-bit binary number, then (x_i) can range from 0 to 15, and the corresponding binary form will be from 0000 to 1111. This step provides a way to encode the solution vector for the probabilistic computer.

[0101] 3. Determine the input signal and update rule: The probability calculation algorithm gradually searches for the minimum value of the objective function by updating the state of the probability bit. The input signal and update rule are determined by taking partial derivatives of the objective loss function with respect to multiple elements of the solution vector. The partial derivatives reflect the trend of the objective function as the elements of the solution vector change, which will guide the update of the probability bit. The input signal reflects the interaction strength between the probability bits and the external effect of a single probability bit, respectively, which are calculated based on the partial derivatives of the objective loss function.

[0102] 4. Determine the probability calculation algorithm: The implementation details of the probability calculation algorithm can be clearly determined by combining the target loss function, the binary solution vector, the input signal, and the update rule of the solution vector. The algorithm usually includes an initialization step, in which each element of the solution vector is randomly assigned to a probability bit string. The algorithm will then iteratively update the state of the probability bit until the target function converges or the number of iterations reaches a preset maximum value.

[0103] For example, the iterative update of the algorithm can follow some random sampling rule, such as Boltzmann sampling, to approximate the minimum value of the objective function with the state evolution of the probability bits. The update process may involve adjusting the weights, biases, or random resets of the probability bits until the most likely binary bit string that satisfies the first linear system solution is found.

[0104] Through these steps, we are able to design a probabilistic calculation algorithm for the first linear system with high computational performance requirements, so that it can be solved effectively on a probabilistic computer. This method fully utilizes the advantages of probabilistic computers in dealing with nonlinear optimization problems and provides a new and efficient solution for solving large-scale Poiseuille flow problems with high precision requirements. The design of the probabilistic calculation algorithm is a key link in the probabilistic-classical hybrid solver, which directly determines the system's solution capability and efficiency in the high-performance subdomain.

[0105] For ease of understanding, here we solve Take the above linear system in dimensional space as an example, and restrict the solution to the positive integer domain, and take , , , , ,but , , . Then, the coefficient matrix is , the bias vector is set to , and assume that each element in the solution vector can be represented by two bits, that is, P=2, Q=0, then , , bring it into the target loss function Get

[0106]

[0107] , that is, we can get an unconstrained optimization problem with a unique solution.

[0108] Objective loss function Taking partial derivatives of the variables separately, we can get their input , as follows:

[0109] , (7.1)

[0110] , (7.2)

[0111] , (7.3)

[0112] , (7.4)

[0113] , (7.5)

[0114] , (7.6)

[0115] , (7.7)

[0116] . (7.8)

[0117] According to the above equation, we can obtain the update criterion In and , as follows: = ,So For the matrix The element in row i and column j in For vector The elements, vector is the initial random bit string.

[0118] Based on the above embodiment, the process of the entire probability calculation algorithm for solving the linear system is as follows:

[0119] 1. Initialize the randomly generated bit string of length 8 as variables The initial value of

[0120] 2. Obtain the input of the probability computer according to equations (7.1-7.8) , , , ;

[0121] 3. According to Get the corresponding output , , , Bit string value, where rand (-1, +1) is a uniform distribution in the interval (-1, +1) that can randomly generate values ​​in the interval (-1, +1), and tan[I i (t)] is the input variable [I i (t)], sgn{x} is the sign function, sgn{x>0}=1 and sgn{x<0 or x=0}=0;

[0122] 4. According to the iteration rules Perform iterative updates, where Select 1 (can be adjusted according to the problem being solved);

[0123] 5. Until output , , , When the distribution of the bit string no longer changes or the maximum number of iterations is reached, the highest probability is output. , , , Bit string value;

[0124] 6. Output the one with the highest probability , , , The solution of the linear system can be obtained by substituting the bit string value into the binary form of the set solution. Therefore, the probability calculation algorithm is used to solve the sublinear system solution in its corresponding subdomain (i.e. the first subdomain solution mentioned above).

[0125] In an exemplary embodiment, solving the second linear system by a classical algorithm to obtain a second subdomain solution includes: running the classical algorithm to obtain the second subdomain solution, wherein the classical algorithm includes one of the following: a chase method, a Gaussian elimination method.

[0126] This embodiment describes how to use a classical algorithm to solve the second linear system divided from the Poiseuille flow problem, that is, a subdomain linear system with relatively low computational performance requirements. The following is a description of the specific steps of using a classical algorithm to solve the second linear system to obtain a second subdomain solution:

[0127] 1. Select a classical algorithm: For the second linear system, select a classical numerical algorithm suitable for solving a system of linear equations. In this embodiment, it is recommended to use the catch-up method or the Gaussian elimination method. Both algorithms are widely used methods in classical numerical analysis, suitable for solving sparse tridiagonal matrix equations, and perform well in scenarios where computing resources and accuracy requirements are not so stringent.

[0128] 1) Chasing method: Applicable to tridiagonal linear systems, it efficiently solves this special type of linear system problem through forward and backward substitution. This algorithm has advantages in both computing speed and memory consumption, especially when the second linear system is not large or the computational accuracy is not high, the chasing method is an ideal choice.

[0129] 2) Gaussian elimination: Applicable to more general linear system equations. Its principle is to transform the system equations into a step matrix form by row transformation of the matrix, and then solve the unknowns by back substitution. Although Gaussian elimination may be less efficient when solving large-scale, dense linear systems, it is still a feasible and effective choice for relatively small and sparse systems such as the second linear system.

[0130] 2. Run the algorithm on a classical computer: Once an appropriate classical algorithm is selected, it can be run on a classical computer to solve the second linear system. Classical computers use bits as the basic unit of information and perform calculations through traditional logic gates and arithmetic units. Therefore, for relatively simple problems such as the second linear system, classical computing is efficient and accurate.

[0131] 3. Obtain the second subdomain solution: Through the operation of the classical algorithm, the classical computer will obtain the numerical result of the second subdomain solution, that is, the solution vector of the second linear system. This solution vector contains the flow velocity values ​​of all discrete points in the second subdomain and can be directly used to solve the subsequent Poiseuille flow problem.

[0132] For example, if the second linear system is solved by the pursuit method, first a forward substitution is performed to transform the system equations into a more easily solvable form, and then a backward substitution is performed to gradually solve each unknown in the solution vector. The resulting solution vector is the second subdomain solution and can be directly used in the overall solution process of the Poiseuille flow problem.

[0133] By solving the second linear system using classical algorithms in a subdomain with relatively low performance requirements, we are able to reduce computational costs and improve overall computational efficiency while retaining high accuracy and reliability. This approach is combined with the strategy of solving high-performance subdomains using probabilistic computing algorithms in a probabilistic-classical hybrid solver, achieving efficient solutions to Poiseuille flow problems while fully leveraging the respective advantages of probabilistic and classical computers.

[0134] Optionally, determining the target solution of the Poiseuille flow equation based on the first subdomain solution and the second subdomain solution includes: performing a boundary continuity check on the first subdomain solution and the second subdomain solution, and adjusting the boundary values ​​of the first subdomain solution and the second subdomain solution according to the check result to obtain an adjusted first subdomain solution and an adjusted second subdomain solution; and sequentially splicing the adjusted first subdomain solution and the adjusted second subdomain solution in the order of multiple subdomains to obtain the target solution.

[0135] This embodiment describes in detail how to fuse the first subdomain solution obtained by the probability calculation algorithm and the second subdomain solution obtained by the classical algorithm to determine the global target solution of the Poiseuille flow equation. The following is a description of the steps of the fusion process:

[0136] 1. Boundary continuity check: Before combining the first subdomain solution and the second subdomain solution, a boundary continuity check is performed first. Since the domain of the Poiseuille flow equation is decomposed into multiple overlapping subdomains, the solution of each subdomain should remain continuous on the overlapping boundaries. This continuity is a direct reflection of the principle of physical continuity in fluid mechanics problems and is crucial to ensuring the physical meaning and accuracy of the solution. The verification step usually includes comparing the flow velocity values ​​of the two subdomain solutions on the overlapping boundary to ensure that they transition smoothly without obvious discontinuities or jumps. If the flow velocity at the boundary is found to be discontinuous, it may be due to the difference in solution accuracy between the probabilistic calculation and the classical calculation near the boundary or the difference in the initial value setting.

[0137] 2. Boundary value adjustment: According to the results of the boundary continuity check, the boundary values ​​of the first subdomain solution and the second subdomain solution are adjusted as necessary. The purpose of the adjustment is to eliminate discontinuities at the boundary and ensure the smoothness and physical rationality of the solution. This is usually achieved by numerical interpolation, averaging on the boundary or according to the continuity conditions in fluid mechanics. For example, a continuous velocity distribution can be generated by taking the average of the flow velocities of the two subdomains on the boundary as the final boundary velocity, or using more complex interpolation methods, such as cubic spline interpolation.

[0138] For example, assuming that the flow velocities of the subdomain solutions at the overlapping boundaries are (u_1) and (u_2), and (u_1 is not equal to u_2), the adjusted boundary flow velocity can be set to (u_1 + u_2) / 2 to ensure the continuity of the flow velocity at the boundary.

[0139] Splicing subdomain solutions: Once the solutions of the two subdomains are adjusted to be continuous on the overlapping boundary, the adjusted solutions of the first subdomain and the second subdomain are spliced ​​in the order of the subdomain division. The result of the splicing forms the solution vector on the entire Poiseuille flow equation definition domain, i.e., the target solution. This splicing process ensures that the solutions of each subdomain are correctly connected in the global solution without physical or numerical discontinuities.

[0140] For example, if the entire definition domain is divided into three subdomains (subdomain 1, subdomain 2, and subdomain 3), where there is overlap between subdomain 1 and subdomain 2 and between subdomain 2 and subdomain 3, then after adjusting the boundary values ​​of all subdomain solutions, the solution vector of subdomain 1, the solution vector of subdomain 2, and the solution vector of subdomain 3 are spliced ​​in sequence to obtain the target solution vector of the Poiseuille flow equation on the entire definition domain.

[0141] Through the above steps, the probability-classical hybrid solver for Poiseuille flow problems can generate a global, physically continuous solution vector as the target solution. This method not only takes advantage of the probabilistic computing in processing high-performance subdomains, but also maintains the accuracy and reliability of classical computing in processing low-performance subdomains, and finally combines an efficient and accurate solution for the entire problem.

[0142] In an optional embodiment, the present application is combined with Figure 4 The solution method of the Poiseuille flow equation is further explained, as follows: Figure 4 As shown, Figure 4 A flow chart of a probabilistic-classical hybrid solver for solving Poiseuille flow problems is shown, comprising the following steps:

[0143] Step 1: Input the Poiseuille flow problem into the probabilistic-classical hybrid solver;

[0144] Step 2, discretize the two-dimensional incompressible Poiseuille flow equation by finite difference to obtain the corresponding linear system;

[0145] Step 3, applying a domain decomposition algorithm to decompose the definition domain of the two-dimensional incompressible Poiseuille flow equation to obtain multiple subdomains;

[0146] Step 4: Determine the performance requirement category of the linear system involved in the subdomain;

[0147] Step 5: If the performance requirement category is high performance requirement (i.e., the first linear system), solve the corresponding sublinear system using a probability algorithm to obtain a first subdomain solution;

[0148] Step 6: If the performance requirement category is low performance requirement (i.e., the second linear system), the corresponding sublinear system is solved using a classical algorithm to obtain a second subdomain solution;

[0149] Step 7: Process the solution of each subdomain to obtain the solution of the Poiseuille flow problem, and complete the solution of the Poiseuille flow problem.

[0150] Through the description of the above implementation methods, those skilled in the art can clearly understand that the method according to the above embodiment can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes a number of instructions for a terminal device (which can be a mobile phone, computer, server, or network device, etc.) to execute the methods described in each embodiment of the present application.

[0151] In this embodiment, a device for determining flow velocity distribution information of a target fluid is also provided. Figure 5 is a structural block diagram of a device for determining flow velocity distribution information of a target fluid according to an embodiment of the present application, such as Figure 5 As shown, the device comprises:

[0152] A construction module 52, configured to construct a Poiseuille flow equation according to fluid parameters of the target fluid, wherein the Poiseuille flow equation is used to determine flow velocity distribution information of the target fluid;

[0153] A conversion module 54 is used to convert the Poiseuille flow equation into linear systems on different subdomains by using a finite difference algorithm and a domain decomposition algorithm to obtain multiple linear systems;

[0154] a solving module 56, configured to solve the first linear system by a probability calculation algorithm to obtain a first subdomain solution, and solve the second linear system by a classical algorithm to obtain a second subdomain solution, wherein the multiple linear systems include the first linear system and the second linear system, the performance requirement of the first linear system is higher than or equal to a preset threshold, the performance requirement of the second linear system is lower than the preset threshold, and the performance requirements of the multiple linear systems are determined according to the subdomain parameters of the different subdomains;

[0155] The determination module 58 is used to determine a target solution of the Poiseuille flow equation according to the first subdomain solution and the second subdomain solution, wherein the target solution is used to indicate flow velocity distribution information of the target fluid.

[0156] Through the above-mentioned device, a Poiseuille flow equation is first constructed according to the fluid parameters of the target fluid, so as to determine the flow velocity distribution information of the target fluid through the Poiseuille flow equation; then, the Poiseuille flow equation is converted into a linear system on different subdomains through a finite difference algorithm and a regional decomposition algorithm to obtain a plurality of linear systems; then, the first linear system is solved through a probability calculation algorithm to obtain a first subdomain solution, and the second linear system is solved through a classical algorithm to obtain a second subdomain solution, wherein the plurality of linear systems include a first linear system and a second linear system, the performance requirement of the first linear system is higher than or equal to a preset threshold, and the performance requirement of the second linear system is lower than the preset threshold, and the performance requirements of these linear systems are based on the subdomains of different subdomains. The parameters are determined; finally, the target solution of the Poiseuille flow equation is determined according to the first subdomain solution and the second subdomain solution, the Poiseuille flow equation is solved, and the flow velocity distribution information of the target fluid is determined; the above scheme is adopted to solve the linear system design corresponding to the high performance requirement, and the linear system involving low performance requirement is solved by the classical algorithm, and the performance advantage of probability calculation and the outstanding performance of classical computers in processing traditional complex computing problems are used to solve the Poiseuille flow problem, so as to improve the efficiency of solving complex problems and reduce the required supercomputing power; thereby solving the problem in the related technology that the current solution method of the Poiseuille flow equation requires huge supercomputing power, which poses a severe challenge to the performance of current classical computers.

[0157] Optionally, the above-mentioned conversion module 54 is also used to discretize the Poiseuille flow equation through the finite difference algorithm to obtain a target linear system and acquire parameter information of the target linear system; decompose the definition domain of the Poiseuille flow equation through the regional decomposition algorithm to obtain multiple subdomains; and discretize the Poiseuille flow equation through the finite difference algorithm in the multiple subdomains according to the parameter information to obtain the multiple linear systems.

[0158] Optionally, the Poiseuille flow equation is , x, y represent the liquid flow direction and longitudinal coordinate respectively, represents the flow velocity in the x direction, represents the fluid density, express The pressure gradient in the direction, represents the viscosity of the fluid, represents time, the boundary condition of the Poiseuille flow equation is: when hour, , h represents the distance between the parallel plate and the center line of the two parallel plates. The above-mentioned conversion module 54 is also used to divide the interval (-h, h) into n+1 parts along the y direction to obtain n+1 sub-intervals, and divide the time t into T parts to obtain T discretized times, wherein the interval interval of each sub-interval is , the discretization time step size for each discretization time ; Use the preset finite difference format to approximate the first and second order derivatives to obtain: , where the superscript + indicates that the velocity at the next time step is unknown, and the subscript , , Respectively indicate along Three adjacent points obtained after direction discretization; apply all discretized points along the y direction to the formula The target linear system is obtained from ,in, matrix, For one dimensional vector, , , , .

[0159] Furthermore, the above-mentioned conversion module 54 is also used to decompose the definition domain into the multiple subdomains through the regional decomposition algorithm, wherein the boundaries of two adjacent subdomains in the multiple subdomains overlap; determine the value ranges of the multiple subdomains, wherein the value ranges include: the coordinate range of the subdomain in the flow direction, and the coordinate range perpendicular to the flow direction; determine the boundary conditions adopted by the Poiseuille flow equation in each subdomain, wherein the boundary conditions include: the restriction conditions of the fluid velocity at the subdomain boundary.

[0160] Optionally, the above-mentioned conversion module 54 is also used to discretize the definition domain of the subdomain into multiple discrete points in each subdomain; perform differential operations on the function values ​​of the Poiseuille flow equation at the multiple discrete points to obtain multiple finite difference expressions; at each discrete point, replace the derivative of the Poiseuille flow equation with the corresponding finite difference expression to obtain the discretized equation at the discrete point; and combine the discretized equations at the multiple discrete points to obtain a linear system.

[0161] Optionally, the above-mentioned solution module 56 is also used to perform parameter analysis on the multiple subdomains to obtain subdomain parameters of the multiple subdomains, and perform parameter analysis on the multiple linear systems to obtain system parameters of the multiple linear systems, wherein the subdomain parameters include: subdomain flow characteristics, complexity of the boundary conditions, and the system parameters include: scale of the linear system, condition number of the linear system; perform performance requirement evaluation on the multiple linear systems according to the subdomain parameters and the system parameters to obtain performance requirements of the multiple linear systems; and classify the multiple linear systems into the first linear system and the second linear system according to the multiple performance requirements and the preset threshold.

[0162] Optionally, the above-mentioned solution module 56 is also used to design the probability calculation algorithm for the first linear system; run the probability calculation algorithm to obtain the binary representation of the first subdomain solution; read the binary representation of the first subdomain solution, and convert the binary representation of the first subdomain solution back to the solution vector of the first linear system to obtain the first subdomain solution.

[0163] Optionally, the above-mentioned solution module 56 is also used to construct a target loss function for solving the first linear system, wherein the minimum value of the target loss function corresponds to the optimal solution of the first linear system; convert the solution vector of the first linear system into binary form to represent multiple elements in the solution vector by a preset number of probability bits; calculate partial derivatives of the multiple elements through the target loss function to determine the input signal of the probability calculation algorithm and the update rule of the solution vector; determine the probability calculation algorithm according to the target loss function, the binary solution vector, the input signal and the update rule.

[0164] Optionally, the above objective loss function includes: = ,in, is the coefficient matrix of the first linear system, is the bias vector of the first linear system, the vector is the solution vector of the first linear system, the vector is a vector The conjugate transpose of .

[0165] Optionally, the solution module 56 is further used to run the classical algorithm to obtain the second subdomain solution, wherein the classical algorithm includes one of the following: a chase method and a Gaussian elimination method.

[0166] Optionally, the above-mentioned determination module 58 is also used to perform boundary continuity check on the first subdomain solution and the second subdomain solution, and adjust the boundary values ​​of the first subdomain solution and the second subdomain solution according to the check result to obtain an adjusted first subdomain solution and an adjusted second subdomain solution; and sequentially splice the adjusted first subdomain solution and the adjusted second subdomain solution in the order of multiple subdomains to obtain the target solution.

[0167] It should be noted that the above modules can be implemented by software or hardware. For the latter, it can be implemented in the following ways, but not limited to: the above modules are all located in the same processor; or the above modules are located in different processors in any combination.

[0168] An embodiment of the present application further provides a computer-readable storage medium, in which a computer program is stored, wherein the computer program is configured to execute the steps of any of the above method embodiments when running.

[0169] In an exemplary embodiment, the computer-readable storage medium may include, but is not limited to, various media that can store computer programs, such as a USB flash drive, a read-only memory (ROM), a random access memory (RAM), a mobile hard disk, a magnetic disk or an optical disk.

[0170] An embodiment of the present application further provides an electronic device, including a memory and a processor, wherein a computer program is stored in the memory, and the processor is configured to run the computer program to execute the steps in any one of the above method embodiments.

[0171] In an exemplary embodiment, the electronic device may further include a transmission device and an input / output device, wherein the transmission device is connected to the processor, and the input / output device is connected to the processor.

[0172] An embodiment of the present application further provides a computer program product, comprising a non-volatile computer-readable storage medium, wherein the non-volatile computer-readable storage medium stores a computer program product, and when the computer program is executed by a processor, the steps of the method described in each embodiment of the present application are implemented.

[0173] For specific examples in this embodiment, reference may be made to the examples described in the above embodiments and exemplary implementation modes, and this embodiment will not be described in detail herein.

[0174] Obviously, those skilled in the art should understand that the above modules or steps of the present application can be implemented by a general computing device, they can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, and in some cases, the steps shown or described can be executed in a different order from that herein, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. Thus, the present application is not limited to any specific combination of hardware and software.

[0175] The above description is only the preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for determining flow velocity distribution information of a target fluid, characterized in that: include: Constructing a Poiseuille flow equation according to fluid parameters of the target fluid, wherein the Poiseuille flow equation is used to determine flow velocity distribution information of the target fluid; The Poiseuille flow equation is converted into a linear system on different subdomains by a finite difference algorithm and a domain decomposition algorithm to obtain multiple linear systems; Solving the first linear system by a probability calculation algorithm to obtain a first subdomain solution, and solving the second linear system by a classical algorithm to obtain a second subdomain solution, wherein the multiple linear systems include the first linear system and the second linear system, the performance requirement of the first linear system is higher than or equal to a preset threshold, the performance requirement of the second linear system is lower than the preset threshold, and the performance requirements of the multiple linear systems are determined according to the subdomain parameters of the different subdomains; A target solution of the Poiseuille flow equation is determined according to the first subdomain solution and the second subdomain solution, wherein the target solution is used to indicate flow velocity distribution information of the target fluid.

2. The method according to claim 1, characterized in that The Poiseuille flow equation is converted into a linear system on different subdomains by a finite difference algorithm and a domain decomposition algorithm to obtain multiple linear systems, including: Discretizing the Poiseuille flow equation by using the finite difference algorithm to obtain a target linear system, and acquiring parameter information of the target linear system; Decomposing the definition domain of the Poiseuille flow equation by the domain decomposition algorithm to obtain a plurality of subdomains; According to the parameter information, the Poiseuille flow equation is discretized in the multiple subdomains by using the finite difference algorithm to obtain the multiple linear systems.

3. The method according to claim 2, characterized in that The Poiseuille flow equation is , x, y represent the liquid flow direction and longitudinal coordinate respectively, represents the flow velocity in the x direction, represents the fluid density, express The pressure gradient in the direction, represents the viscosity of the fluid, represents time, the boundary condition of the Poiseuille flow equation is: when hour, , h represents the distance between the parallel plate and the center line of the two parallel plates, The method of discretizing the Poiseuille flow equation by the finite difference algorithm to obtain a target linear system includes: Divide the interval (-h, h) into n+1 parts along the y direction, and obtain n+1 sub-intervals, and divide the time t into T parts, and obtain T discretized times, where the interval interval of each sub-interval is , the discretization time step size for each discretization time ; Using the preset finite difference scheme to approximate the first and second order derivatives, we get: , where the superscript + indicates that the velocity at the next time step is unknown, and the subscript , , Respectively indicate along Three adjacent points obtained after direction discretization; Apply the formula to all discretized points along the y direction The target linear system is obtained from ,in, matrix, For one dimensional vector, , , , .

4. The method according to claim 2, characterized in that: The domain of the Poiseuille flow equation is decomposed by the domain decomposition algorithm to obtain multiple subdomains, including: Decomposing the definition domain into the multiple subdomains by using the region decomposition algorithm, wherein the boundaries of two adjacent subdomains in the multiple subdomains overlap; Determine the value ranges of the multiple subdomains, wherein the value ranges include: the coordinate range of the subdomains in the flow direction, and the coordinate range perpendicular to the flow direction; The boundary conditions adopted by the Poiseuille flow equation in each subdomain are determined, wherein the boundary conditions include: restriction conditions of fluid velocity at the subdomain boundary.

5. The method according to claim 4, characterized in that The Poiseuille flow equation is discretized by the finite difference algorithm in the multiple subdomains to obtain the multiple linear systems, including: In each subdomain, the definition domain of the subdomain is discretized into multiple discrete points; performing differential operations on the function values ​​of the Poiseuille flow equation at the plurality of discrete points to obtain a plurality of finite difference expressions; At each discrete point, the derivative of the Poiseuille flow equation is replaced by a corresponding finite difference expression to obtain a discretized equation at the discrete point; The discretized equations at the plurality of discrete points are combined to obtain a linear system.

6. The method according to claim 4, characterized in that Before solving the first linear system by a probability calculation algorithm to obtain a first subdomain solution and solving the second linear system by a classical algorithm to obtain a second subdomain solution, the method further includes: Performing parameter analysis on the multiple subdomains to obtain subdomain parameters of the multiple subdomains, and performing parameter analysis on the multiple linear systems to obtain system parameters of the multiple linear systems; Performing performance requirement evaluation on the multiple linear systems according to the subdomain parameters and the system parameters to obtain performance requirements of the multiple linear systems; The plurality of linear systems are classified into the first linear system and the second linear system according to the plurality of performance requirements and the preset threshold.

7. The method according to claim 1, characterized in that The method of solving the first linear system by using a probability calculation algorithm to obtain a first subdomain solution includes: Designing the probability calculation algorithm for the first linear system; Running the probability calculation algorithm to obtain a binary representation of the first subdomain solution; The binary representation of the first subdomain solution is read, and the binary representation of the first subdomain solution is converted back into a solution vector of the first linear system to obtain the first subdomain solution.

8. The method according to claim 7, characterized in that Designing the probability calculation algorithm for the first linear system includes: Constructing an objective loss function for solving the first linear system, wherein a minimum value of the objective loss function corresponds to an optimal solution of the first linear system; Converting the solution vector of the first linear system into binary form to represent multiple elements in the solution vector by a preset number of probability bits; Taking partial derivatives of the multiple elements through the target loss function to determine an input signal of the probability calculation algorithm and an update rule of the solution vector; The probability calculation algorithm is determined according to the target loss function, the solution vector in binary form, the input signal and the update rule.

9. The method according to claim 8, characterized in that The target loss function includes: = ,in, is the coefficient matrix of the first linear system, is the bias vector of the first linear system, the vector is the solution vector of the first linear system, the vector is a vector The conjugate transpose of .

10. The method according to claim 1, characterized in that The second linear system is solved by a classical algorithm to obtain a second subdomain solution, including: Run the classical algorithm to obtain the second subdomain solution, wherein the classical algorithm includes one of the following: a chase method and a Gaussian elimination method.

11. The method according to claim 1, characterized in that: Determining a target solution of the Poiseuille flow equation according to the first subdomain solution and the second subdomain solution includes: Performing a boundary continuity check on the first subdomain solution and the second subdomain solution, and adjusting boundary values ​​of the first subdomain solution and the second subdomain solution according to the check result to obtain an adjusted first subdomain solution and an adjusted second subdomain solution; The adjusted first subdomain solution and the adjusted second subdomain solution are sequentially spliced ​​in the order of the multiple subdomains to obtain the target solution.

12. A device for determining flow velocity distribution information of a target fluid, characterized in that: include: A construction module, used to construct a Poiseuille flow equation according to fluid parameters of the target fluid, wherein the Poiseuille flow equation is used to determine flow velocity distribution information of the target fluid; A conversion module, used for converting the Poiseuille flow equation into linear systems on different subdomains through a finite difference algorithm and a domain decomposition algorithm to obtain multiple linear systems; a solution module, configured to solve the first linear system by a probability calculation algorithm to obtain a first subdomain solution, and solve the second linear system by a classical algorithm to obtain a second subdomain solution, wherein the multiple linear systems include the first linear system and the second linear system, the performance requirement of the first linear system is higher than or equal to a preset threshold, the performance requirement of the second linear system is lower than the preset threshold, and the performance requirements of the multiple linear systems are determined according to the subdomain parameters of the different subdomains; A determination module is used to determine a target solution of the Poiseuille flow equation according to the first subdomain solution and the second subdomain solution, wherein the target solution is used to indicate flow velocity distribution information of the target fluid.

13. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, wherein the computer program implements the steps of the method according to any one of claims 1 to 11 when executed by a processor.

14. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 11 are implemented.

15. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 11 are implemented.

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