Lattice Boltzmann method and device based on entropy optimized relaxation model

Abstract

This invention relates to a lattice Boltzmann method, apparatus, computer device, and storage medium based on an entropy-optimized relaxation model. First, the distribution function before the collision is obtained and cumulant transformation is performed to obtain higher-order and lower-order cumulants. The higher-order cumulants capture more flow details. The local entropy value of the higher-order cumulants is maximized through entropy optimization, and the relaxation coefficient is adjusted to ensure the stability and accuracy of the simulation. Then, the lower-order and optimized higher-order cumulants are subjected to inverse cumulant transformation to obtain the distribution function after the collision. Finally, the post-collision distribution function is migrated between grid points and updated to simulate the fluid flow process. This invention improves the accuracy and stability of the simulation, reduces numerical oscillations and error accumulation, and provides an effective solution, particularly for high Reynolds number flows and complex geometries, offering new ideas and methods for future fluid dynamics simulations.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and in particular to a lattice Boltzmann method, device, computer equipment and storage medium based on an entropy optimized relaxation model. Background Art

[0002] The lattice Boltzmann method (LBM) has made significant progress in numerical fluid dynamics simulation and is widely used due to its algorithmic simplicity and efficient parallel computing capabilities. However, existing LBM methods often face challenges in numerical stability and computational efficiency when simulating high Reynolds number flows and complex geometries. In particular, in collision models with high-order cumulants, due to the lack of appropriate relaxation coefficients, the simulation results are prone to numerical oscillations and instability, which limits the widespread application and development of LBM in practical applications.

[0003] Although some studies have tried to improve the high-order cumulants collision model by introducing the entropy optimization principle, hoping to determine the relaxation coefficient by maximizing the local entropy value and improve the simulation accuracy and stability, these methods still have significant problems in practice. One major problem is how to balance the contradiction between accuracy and stability in the calculation process of high-order cumulants. The relaxation coefficient of high-order cumulants is difficult to determine, which can easily lead to numerical oscillation and affect the overall simulation effect.

[0004] In addition, existing entropy optimization methods may introduce additional numerical errors when inversely transforming back to the distribution function. These errors may accumulate and reduce the accuracy and stability of the calculation, especially in long-term simulations or large-scale complex flow problems. Therefore, the current LBM still faces technical bottlenecks in the face of the demand for high-precision and high-stability fluid simulation. Summary of the invention

[0005] The main purpose of the present invention is to provide a lattice Boltzmann method, device, computer equipment and storage medium based on an entropy optimized relaxation model to solve the problems of poor numerical stability and low computational efficiency often faced by existing LBM methods when simulating high Reynolds number flows and complex geometric shapes.

[0006] To achieve the above-mentioned purpose, the present invention provides a lattice Boltzmann method based on an entropy optimized relaxation model, comprising the following steps: obtaining a distribution function before a collision, and performing a cumulant transformation process on the distribution function to obtain a plurality of cumulants, wherein the plurality of cumulants include a high-order cumulant and a low-order cumulant; maximizing the local entropy value of the high-order cumulant by an entropy optimization process to obtain an optimized high-order cumulant; performing an inverse transformation process on the low-order cumulant and the optimized high-order cumulant by an inverse cumulant transformation formula to obtain a distribution function after a collision; migrating the distribution function after a collision in a physical space, and updating the distribution function of each grid point.

[0007] Further, the distribution function is subjected to cumulant transformation processing to obtain multiple cumulants, including: the distribution function is subjected to cumulant transformation processing to obtain low-order cumulants and high-order cumulants, wherein the low-order cumulants are expressed as: , the high-order cumulant is: , the low-order cumulant is a cumulant of order 3 or below.

[0008] Further, an entropy optimization processing method is used to maximize the local entropy value of the high-order cumulant to obtain an optimized high-order cumulant, including: using a first formula to maximize the local entropy value of the high-order cumulant to obtain an optimized high-order cumulant, wherein the first formula is: ,in, It is the optimized high-order cumulative amount. The high-order cumulative amount after entropy optimization is the result we need to calculate. is the identity matrix, which has the same dimensions as the short matrix Same, here used for matrix addition operations. Represents the coefficient matrix of a certain linear operation. In this formula, it is used to correct the calculation of the cumulant. D is a diagonal matrix consisting of the identity matrix and the zero matrix. Its form is: , which is used to select a specific portion of the cumulant in the calculation. is the transpose of matrix D. Since This is just a Swap rows and columns. Represents the grid weight, which is used to weigh the weights of different distribution functions during entropy optimization. It is the inverse matrix of the weight matrix W. It is used to adjust the influence of different weights. A transformation matrix representing higher-order cumulants, which is used to relate distribution functions to higher-order cumulants. The transformation matrix representing the low-order cumulants is used to relate the distribution function to the low-order cumulants. It is a low-order cumulant. The low-order part obtained by cumulant transformation is used to calculate the high-order cumulant during the optimization process. Used to correct the calculation results of high-order cumulants. It is obtained from the following relationship: m represents the relationship between the distribution function f and the cumulant k, defined as m = nk. The transformation matrix T is used to transform the distribution function into the central moment, which can be decomposed into: ,in, and are the transformation matrices of low-order and high-order cumulants respectively.

[0009] Furthermore, after maximizing the local entropy value of the high-order cumulant by adopting the entropy optimization processing method to obtain the optimized high-order cumulant, the lattice Boltzmann method further includes: introducing a preset constraint condition, and adaptively adjusting the optimized high-order cumulant based on the preset constraint condition to ensure that the optimized high-order cumulant does not deviate from the equilibrium state and the cumulant range before the collision, wherein the preset constraint condition is .

[0010] Furthermore, the optimized high-order cumulants are adaptively adjusted based on the preset constraints, including: determining whether the optimized high-order cumulants exceed the preset constraints; if not, continuing to execute the step of "using the inverse cumulant transformation formula to inversely transform the low-order cumulants and the optimized high-order cumulants to obtain a post-collision distribution function"; if exceeded, adopting a smoothing correction strategy to adjust the optimized high-order cumulants to within the preset constraints.

[0011] Furthermore, a smooth correction strategy is adopted to adjust the optimized high-order cumulative amount to within the preset constraint range, including: when adopting a smooth correction strategy to adjust the optimized high-order cumulative amount to within the preset constraint range, an entropy correction function is introduced to ensure that when correcting the high-order cumulative amount, the entropy value always increases or remains unchanged.

[0012] Furthermore, after migrating the distribution function after the collision in the physical space and updating the distribution function of each grid point, the lattice Boltzmann method also includes: using the updated distribution function as the distribution function before the collision, and re-executing the step of "performing a cumulative amount transformation on the distribution function to obtain multiple cumulative amounts" to continuously iterate the fluid dynamic behavior represented by the distribution function.

[0013] The present invention also provides a lattice Boltzmann device based on an entropy optimized relaxation model, comprising: an acquisition unit, used to acquire a distribution function before a collision, and perform a cumulant transformation process on the distribution function to obtain a plurality of cumulants, wherein the plurality of cumulants include a high-order cumulant and a low-order cumulant; an optimization unit, used to maximize the local entropy value of the high-order cumulant using an entropy optimization process to obtain an optimized high-order cumulant; a processing unit, used to perform an inverse transformation process on the low-order cumulant and the optimized high-order cumulant using an inverse cumulant transformation formula to obtain a distribution function after a collision; and a migration unit, used to migrate the distribution function after a collision in a physical space, and update the distribution function of each grid point.

[0014] The present invention also provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of any one of the above methods when executing the computer program.

[0015] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of any of the above-mentioned methods are implemented.

[0016] The present invention provides a lattice Boltzmann method, device, computer equipment and storage medium based on an entropy optimized relaxation model. First, a distribution function before a collision is obtained, and a cumulant transformation process is performed on the distribution function to obtain multiple cumulants, including high-order and low-order cumulants. The cumulant transformation process involves converting the distribution function into cumulants through mathematical transformation. These cumulants can better describe the local characteristics of the fluid, especially high-order cumulants can capture more flow details.

[0017] Next, the entropy optimization method is used to maximize the local entropy value of the high-order cumulants to obtain the optimized high-order cumulants. The core idea of ​​this step is to maximize the local entropy value by adjusting the relaxation coefficient of the high-order cumulants, thereby ensuring the stability and accuracy of the simulation. This process involves solving an optimization problem and determining the optimal relaxation coefficient by maximizing the entropy value.

[0018] Then, the inverse cumulant transformation formula is used to inversely transform the low-order cumulant and the optimized high-order cumulant to obtain the distribution function after the collision. The purpose of the inverse cumulant transformation is to convert the cumulant back into a distribution function for use in subsequent calculations.

[0019] Finally, the distribution function after the collision is migrated in the physical space, and the distribution function of each grid point is updated. The migration process is to propagate the distribution function after the collision between grid points according to the motion law of the fluid, thereby simulating the flow process of the fluid. The distribution function of the grid point is updated to prepare for the next step of calculation, so that the entire simulation process is cyclical.

[0020] The embodiments of the present application improve the processing method of high-order cumulants through the entropy optimization principle, significantly improve the accuracy and stability of the simulation, and reduce the problems of numerical oscillation and error accumulation. By maximizing the local entropy value, the relaxation coefficient of the high-order cumulants is optimized, so that the simulation shows higher stability and accuracy in high Reynolds number flows and complex geometries.

[0021] In general, this lattice Boltzmann method based on the entropy-optimized relaxation model provides an effective solution to the requirements of high-precision and high-stability fluid simulation, and shows significant progress in the simulation of high Reynolds number flows and complex geometries. This not only solves some key problems in the existing technology, but also provides new ideas and methods for future fluid mechanics simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Schematic diagram of the steps of a lattice Boltzmann method based on an entropy optimized relaxation model in one embodiment of the present invention;

[0023] Figure 2 is a block diagram of a lattice Boltzmann device based on an entropy optimized relaxation model in one embodiment of the present invention;

[0024] Figure 3 It is a schematic block diagram of the structure of a computer device according to an embodiment of the present invention.

[0025] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0027] Reference Figure 1 , the embodiment of the present application provides a lattice Boltzmann method based on an entropy optimized relaxation model, comprising the following steps:

[0028] S1, obtaining a distribution function before a collision, and performing a cumulant transformation process on the distribution function to obtain a plurality of cumulants, wherein the plurality of cumulants include a high-order cumulant and a low-order cumulant.

[0029] S2, using an entropy optimization processing method to maximize the local entropy value of the high-order cumulant to obtain an optimized high-order cumulant.

[0030] S3, using an inverse cumulant transformation formula, performing inverse transformation processing on the low-order cumulant and the optimized high-order cumulant to obtain a distribution function after collision.

[0031] S4, performing migration processing on the distribution function after the collision in the physical space, and updating the distribution function of each grid point.

[0032] That is, the embodiment of the present application provides a lattice Boltzmann method based on the entropy optimized relaxation model. First, the distribution function before the collision is obtained, and the distribution function is subjected to a cumulant transformation process to obtain multiple cumulants, including high-order and low-order cumulants. The cumulant transformation process involves converting the distribution function into cumulants through mathematical transformation. These cumulants can better describe the local characteristics of the fluid, especially the high-order cumulants can capture more flow details.

[0033] Next, the entropy optimization method is used to maximize the local entropy value of the high-order cumulants to obtain the optimized high-order cumulants. The core idea of ​​this step is to maximize the local entropy value by adjusting the relaxation coefficient of the high-order cumulants, thereby ensuring the stability and accuracy of the simulation. This process involves solving an optimization problem and determining the optimal relaxation coefficient by maximizing the entropy value.

[0034] Then, the inverse cumulant transformation formula is used to inversely transform the low-order cumulant and the optimized high-order cumulant to obtain the distribution function after the collision. The purpose of the inverse cumulant transformation is to convert the cumulant back into a distribution function for use in subsequent calculations.

[0035] Finally, the distribution function after the collision is migrated in the physical space, and the distribution function of each grid point is updated. The migration process is to propagate the distribution function after the collision between grid points according to the motion law of the fluid, thereby simulating the flow process of the fluid. The distribution function of the grid point is updated to prepare for the next step of calculation, so that the entire simulation process is cyclical.

[0036] The embodiments of the present application improve the processing method of high-order cumulants through the entropy optimization principle, significantly improve the accuracy and stability of the simulation, and reduce the problems of numerical oscillation and error accumulation. By maximizing the local entropy value, the relaxation coefficient of the high-order cumulants is optimized, so that the simulation shows higher stability and accuracy in high Reynolds number flows and complex geometries.

[0037] In general, this lattice Boltzmann method based on the entropy-optimized relaxation model provides an effective solution to the requirements of high-precision and high-stability fluid simulation, and shows significant progress in the simulation of high Reynolds number flows and complex geometries. This not only solves some key problems in the existing technology, but also provides new ideas and methods for future fluid mechanics simulation.

[0038] In one example, performing a cumulant transformation process on the distribution function to obtain a plurality of cumulants includes: performing a cumulant transformation process on the distribution function to obtain a low-order cumulant and a high-order cumulant, wherein the low-order cumulant is expressed as: , the high-order cumulant is: , the low-order cumulant is a cumulant of order 3 or below.

[0039] In this example, the distribution function is transformed by cumulants to obtain multiple cumulants, including low-order cumulants and high-order cumulants. Cumulants transformation converts the distribution function into a more manageable mathematical form for use in subsequent calculations. Low-order cumulants are usually cumulants of order 3 or less, while high-order cumulants are cumulants of higher order.

[0040] It should be noted that low-order cumulants involve lower-order statistics of the distribution function, such as mean and variance. Low-order cumulants are usually more stable, easier to handle, and less likely to introduce numerical errors. The calculation formula for low-order cumulants can be expressed as: ,here, represents the low-order cumulant, is the specific value of the cumulative amount, is a collection containing indices of low-order cumulants. Typically, low-order cumulants include cumulants of order 3 and below. These cumulants can better describe basic properties of the fluid, such as density and momentum.

[0041] It should be noted that high-order cumulants involve higher-order statistics of the distribution function, such as skewness and kurtosis. High-order cumulants can capture more details in the distribution function, but they are prone to numerical oscillation and instability in the calculation. The calculation formula of high-order cumulants can be expressed as: here, represents a high-order cumulant, is the specific value of the cumulative amount, is a collection of indices of higher-order cumulants. The computation of higher-order cumulants is usually more complex and requires advanced numerical methods, such as entropy optimization, to ensure their stability and accuracy.

[0042] In one example, an entropy optimization processing method is used to maximize the local entropy value of the high-order cumulant to obtain an optimized high-order cumulant, including: using a first formula to perform local entropy maximization processing on the high-order cumulant to obtain an optimized high-order cumulant.

[0043] Among them, the first formula is: .

[0044] In this example, an entropy optimization method is used to maximize the local entropy value of the high-order cumulant to obtain an optimized high-order cumulant. The specific process includes using the first formula to maximize the local entropy value of the high-order cumulant to obtain an optimized high-order cumulant.

[0045] The purpose of this step is to adjust the high-order cumulants The calculation method maximizes the local entropy value, thereby improving the accuracy and stability of the simulation. The following is a detailed explanation of each part of the formula:

[0046] This is an inverse matrix operation where is the identity matrix, is a specific matrix. The purpose of this part is to preprocess the cumulant to facilitate subsequent optimization calculations.

[0047] This involves matrix D and weight matrix and the transformation matrix The combination of these matrices is used to transform the higher-order cumulants to ensure that they accurately reflect the local fluid properties during the entropy optimization process.

[0048] This step is the inverse operation of the above transformation matrix, which is used to convert the transformed result back into the cumulative form.

[0049] This is a low-order cumulant A series of matrix operations are performed to ensure that low-order cumulants can also play a role in the optimization process and provide stable basic data.

[0050] It is an adjustment term used to further modify the high-order cumulants to achieve the goal of maximizing the entropy value.

[0051] Through the above steps, the calculation of high-order cumulants can be optimized, which can significantly improve the numerical stability and calculation accuracy in the simulation of high Reynolds number flows and complex geometries. This method effectively solves the problems of numerical oscillation and instability when dealing with high-order cumulants through the entropy optimization principle, making the application of LBM in complex fluid simulation more extensive and reliable.

[0052] In one example, after maximizing the local entropy value of the high-order cumulant by adopting the entropy optimization processing method to obtain the optimized high-order cumulant, the lattice Boltzmann method further includes: introducing a preset constraint condition, and adaptively adjusting the optimized high-order cumulant based on the preset constraint condition to ensure that the optimized high-order cumulant does not deviate from the equilibrium state and the cumulant range before the collision, wherein the preset constraint condition is .

[0053] In this example, after the entropy optimization method is used to maximize the local entropy value of the high-order cumulants and obtain the optimized high-order cumulants, the lattice Boltzmann method further includes introducing preset constraints and adaptively adjusting the optimized high-order cumulants based on these preset constraints to ensure that the optimized high-order cumulants do not deviate from the equilibrium state and the cumulant range before the collision. Here, represents the optimized high-order cumulant, and Represent the minimum and maximum values ​​of the high-order cumulants respectively. Through this constraint, the optimized high-order cumulants can be ensured Always keep it within a reasonable range, without numerical oscillation and instability. This constraint is very important in actual operation, because when performing entropy optimization, if it is not constrained, the optimization process may cause the high-order cumulants to deviate from their reasonable physical range, thus affecting the stability and accuracy of the overall simulation. By introducing this constraint, the range of variation of the high-order cumulants can be effectively controlled to keep it within a physically reasonable range, thereby ensuring the stability and reliability of the simulation.

[0054] Specifically, when the optimized high-order cumulant After calculating, we need to check whether it is within the preset range. Beyond range, adaptive adjustments need to be made to bring it back within this range. This step can be done in the following ways: Less than , then adjust it to ;if Greater than , then adjust it to ;if exist Through the above adaptive adjustment process, it can ensure that the optimized high-order accumulation It is always within the preset reasonable range, thus improving the numerical stability and simulation accuracy of the entire lattice Boltzmann method.

[0055] It should be noted that the maximum and minimum values ​​of the cumulant can be determined by physical boundary conditions. For example, in fluid mechanics problems, the reasonable range of the cumulant can be derived based on the physical properties of the fluid (such as density, velocity, pressure, etc.). These physical boundary conditions provide the theoretical limit values ​​of the cumulant under different conditions.

[0056] In one example, the optimized high-order cumulant is adaptively adjusted based on the preset constraint conditions, including: determining whether the optimized high-order cumulant exceeds the preset constraint conditions; if not, continuing to execute the step of "using the inverse cumulant transformation formula to inversely transform the low-order cumulant and the optimized high-order cumulant to obtain a post-collision distribution function"; if exceeded, using a smoothing correction strategy to adjust the optimized high-order cumulant to within the preset constraint conditions.

[0057] In the lattice Boltzmann method, in order to ensure that the optimized high-order cumulants remain within the preset reasonable range to avoid numerical oscillation and instability, it is necessary to perform adaptive adjustments. The specific steps are as follows: First, you need to check the optimized high-order cumulants. Whether it exceeds the preset constraints, that is, The purpose of this step is to determine whether the cumulant is within a reasonable range. If the optimized high-order cumulant If the preset constraint range is not exceeded, the next step can be performed, that is, the inverse cumulant transformation formula is used to perform inverse transformation processing on the low-order cumulant and the optimized high-order cumulant to obtain the distribution function after the collision.

[0058] However, if the optimized high-order cumulants If it exceeds the preset constraint range, adaptive adjustment is required. At this time, a smooth correction strategy is needed to adjust the optimized high-order cumulant to the preset constraint range. Specifically, when Lower than , raise it to ;when Higher than , reducing it to This smoothing correction strategy ensures that the high-order cumulants always remain within a physically reasonable range, thus ensuring the stability of the numerical calculation and the simulation accuracy.

[0059] In this way, the range of variation of high-order cumulants can be effectively controlled to ensure that they do not deviate from the range of cumulants in equilibrium and before collision. This treatment method is of great significance in improving the stability and reliability of numerical simulations, and helps to achieve more accurate and stable results in the simulation of high Reynolds number flows and complex geometries.

[0060] In one example, a smooth correction strategy is adopted to adjust the optimized high-order cumulants to within the preset constraint range, including: when adopting the smooth correction strategy to adjust the optimized high-order cumulants to within the preset constraint range, an entropy correction function is introduced to ensure that when correcting the high-order cumulants, the entropy value always increases or remains unchanged.

[0061] In this example, in order to ensure that the optimized high-order cumulants remain within the preset constraints while ensuring numerical stability and computational accuracy, a smoothing correction strategy is required for adjustment. Specifically, this process is not just a simple adjustment of the high-order cumulants to the preset range, but also requires the introduction of an entropy correction function to ensure that when correcting the high-order cumulants, the entropy value always increases or remains unchanged, thereby avoiding numerical oscillation and instability. First, check the optimized high-order cumulants. Whether it exceeds the preset constraints When , if it exceeds this range, it needs to be adjusted. The core idea of ​​the smoothing correction strategy is to correct the high-order cumulant through the entropy correction function to bring it back to the preset reasonable range. Specifically, the entropy correction function S( ) is introduced to ensure that the entropy value (the disorder or information content of the system) always increases or remains unchanged during the correction process. This means that the corrected high-order cumulants not only meet the physical boundary conditions, but also ensure the stability and consistency of the system. Assumption If it exceeds the preset constraint range, the correction process is as follows: Lower than First, raise it to , but this adjustment is not a simple assignment operation, but through the entropy correction function S( ) is completed. The entropy correction function calculates a correction value based on the current system state, so that Promote to At the same time, the entropy value increases or remains unchanged; when Higher than , reducing it to Again, this adjustment is done by correcting the number of entropy graphs S ( ) to achieve this. The entropy correction function will calculate an appropriate correction value so that Reduce to In the process of correction, the entropy value increases or remains unchanged. By introducing the entropy correction function, the smooth correction strategy not only ensures that the high-order cumulant is within the preset range, but also maintains the entropy stability of the system. This processing method helps to avoid the introduction of new numerical errors or unstable factors in the correction process, ensuring the reliability and accuracy of numerical simulation.

[0062] In summary, by introducing the entropy correction function, the reasonable range of the cumulative amount and the stability of the system entropy value are ensured when the optimized high-order cumulative amount is smoothly corrected. In this way, not only the physical rationality of the cumulative amount is guaranteed, but also the overall stability and accuracy of the numerical simulation are improved, especially when dealing with high Reynolds number flows and complex geometric shapes.

[0063] It should be noted that the entropy correction function S( ) is a design for correcting high-order cumulants Its main goal is to adjust , so that it returns to the preset constraint range While ensuring that the entropy value (amount of information or disorder) of the system increases or remains unchanged:

[0064] In one example, after migrating the post-collision distribution function in the physical space and updating the distribution function of each grid point, the lattice Boltzmann method further includes: using the updated distribution function as the pre-collision distribution function, and re-executing the step of "performing a cumulant transformation on the distribution function to obtain multiple cumulants" to continuously iterate the fluid dynamic behavior represented by the distribution function.

[0065] In this example, after the distribution function after the collision is migrated in the physical space and the distribution function of each grid point is updated, the process of the lattice Boltzmann method also includes an iteration step. Specifically, the updated distribution function is used as the new pre-collision distribution function, and the step of "transforming the distribution function by cumulants to obtain multiple cumulants" is re-executed. This iteration process continues to simulate the dynamic behavior of the fluid.

[0066] In other words, in the lattice Boltzmann method, the movement of the fluid is simulated by the collision and migration of microscopic particles. At each time step, the distribution function first experiences a collision and then migrates to the adjacent grid point in physical space. The updated distribution function represents the state of the fluid at the current moment. In order to simulate the behavior of the fluid in subsequent time steps, iterative calculations must be continued.

[0067] At each time step, the distribution function after the collision needs to be migrated to the adjacent grid points. This step simulates the movement of fluid microparticles, causing the fluid state to change in space. Specifically, the value of the distribution function at each grid point is updated to the partial value of the distribution function of its neighboring grid points. As a result of this step, the updated distribution function reflects the distribution of the fluid in the entire computational domain at the current moment.

[0068] After the migration process is completed, the updated distribution function is used as the new pre-collision distribution function for the calculation of the next time step. This means that at the end of each time step, the current fluid state will be used as the initial state for the next calculation. Then, the new pre-collision distribution function is transformed by cumulants to obtain multiple cumulants. These cumulants include low-order cumulants and high-order cumulants, which describe different statistical properties of the fluid.

[0069] Through this iterative process, the lattice Boltzmann method can effectively simulate the dynamic behavior of the fluid. The calculation results of each time step will affect the fluid state of the subsequent time step, thus gradually showing the movement and changes of the fluid in the entire computational domain. This iterative process enables the lattice Boltzmann method to handle complex fluid mechanics problems and provide high-precision numerical simulation results.

[0070] Reference Figure 2 , an embodiment of the present invention provides a lattice Boltzmann device based on an entropy optimized relaxation model, comprising:

[0071] The acquisition unit 1 is used to acquire the distribution function before the collision, and perform cumulant transformation processing on the distribution function to obtain multiple cumulants, wherein the multiple cumulants include high-order cumulants and low-order cumulants.

[0072] The optimization unit 2 is used to maximize the local entropy value of the high-order cumulant by adopting an entropy optimization processing method to obtain an optimized high-order cumulant.

[0073] The processing unit 3 is used to use an inverse cumulant transformation formula to perform inverse transformation processing on the low-order cumulant and the optimized high-order cumulant to obtain a distribution function after collision.

[0074] The migration unit 4 is used to migrate the distribution function after the collision in the physical space and update the distribution function of each grid point.

[0075] In this embodiment, for the specific implementation of each unit in the above device embodiment, please refer to the above method embodiment, which will not be repeated here.

[0076] Reference Figure 3 In an embodiment of the present invention, a computer device is also provided. The computer device may be a server, and its internal structure may be as follows: Figure 3As shown. The computer device includes a processor, a memory, a display screen, an input device, a network interface and a database connected through a system bus. Among them, the processor designed by the computer is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store the corresponding data in this embodiment. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the above method is implemented.

[0077] Those skilled in the art will understand that Figure 3 The structure shown in the figure is merely a block diagram of a portion of the structure related to the solution of the present invention, and does not constitute a limitation on the computer device to which the solution of the present invention is applied.

[0078] An embodiment of the present invention further provides a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the above method is implemented. It can be understood that the computer-readable storage medium in this embodiment can be a volatile readable storage medium or a non-volatile readable storage medium.

[0079] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media provided by the present invention and used in the embodiments may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double-speed data rate SDRAM (SSRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM.

[0080] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, device, article or method including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, device, article or method. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the presence of other identical elements in the process, device, article or method including the element.

[0081] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A lattice Boltzmann method based on an entropy-optimized relaxation model, characterized in that: The following steps are involved: Acquire a distribution function before the collision, and perform cumulant transformation processing on the distribution function to obtain a plurality of cumulants, wherein the plurality of cumulants include a high-order cumulant and a low-order cumulant; The entropy optimization processing method is used to maximize the local entropy value of the high-order cumulant to obtain the optimized high-order cumulant; the entropy optimization processing method is used to maximize the local entropy value of the high-order cumulant to obtain the optimized high-order cumulant, including: The first formula is used to maximize the local entropy value of the high-order cumulant to obtain an optimized high-order cumulant, and the first formula is: ,in, is the optimized high-order cumulant, the high-order cumulant after entropy optimization; is the identity matrix, used for addition of matrix operations; is a coefficient matrix used to modify the calculation of the cumulant; D is a diagonal matrix consisting of the identity matrix and the zero matrix, used to select a specific cumulant part; Represents the grid weight, which is used to measure the weights of different distribution functions; The transformation matrix representing the higher-order cumulants is used to relate the distribution function to the higher-order cumulants; The transformation matrix representing the low-order cumulants is used to relate the distribution function to the low-order cumulants; It is the low-order cumulant. The low-order part obtained by cumulant transformation is used to calculate the high-order cumulant during the optimization process. The calculation results for correcting the higher-order cumulants are obtained from the following relationship: ; The transformation matrix T is used to convert the distribution function into the central moment and can be decomposed into: ; Using an inverse cumulant transformation formula, inverse transformation processing is performed on the low-order cumulant and the optimized high-order cumulant to obtain a distribution function after collision; The post-collision distribution function is migrated in the physical space, and the distribution function of each grid point is updated. The post-collision distribution function is migrated in the physical space, and the distribution function of each grid point is updated. The method also includes, at each time step, first migrating the post-collision distribution function to the adjacent grid point to simulate the movement of fluid microscopic particles, so that the fluid state changes in space.

2. The lattice Boltzmann method according to claim 1, characterized in that: After maximizing the local entropy value of the high-order cumulant by adopting the entropy optimization processing method to obtain the optimized high-order cumulant, the lattice Boltzmann method further includes: Introducing preset constraints, and adaptively adjusting the optimized high-order cumulants based on the preset constraints to ensure that the optimized high-order cumulants do not deviate from the equilibrium state and the cumulant range before the collision, Among them, the preset constraint condition is , represents the optimized high-order cumulant, and Represent the minimum and maximum values ​​of the higher-order cumulants, respectively.

3. The lattice Boltzmann method according to claim 2, characterized in that: Adaptively adjusting the optimized high-order cumulants based on the preset constraint conditions includes: Determining whether the optimized high-order cumulative amount exceeds the preset constraint condition; If it does not exceed, continue to execute the step of "using the inverse cumulant transformation formula to perform inverse transformation processing on the low-order cumulant and the optimized high-order cumulant to obtain the distribution function after collision"; If it has been exceeded, a smoothing correction strategy is adopted to adjust the optimized high-order cumulative amount to within the preset constraint condition range.

4. The lattice Boltzmann method according to claim 3, characterized in that: A smoothing correction strategy is adopted to adjust the optimized high-order cumulative amount to within the preset constraint condition range, including: When the smoothing correction strategy is adopted to adjust the optimized high-order cumulative amount to within the preset constraint condition range, an entropy correction function is introduced to ensure that the entropy value always increases or remains unchanged when correcting the high-order cumulative amount.

5. The lattice Boltzmann method according to claim 1, characterized in that: After the distribution function after the collision is migrated in the physical space and the distribution function of each grid point is updated, the lattice Boltzmann method further includes: The updated distribution function is used as the distribution function before the collision, and the step of "performing a cumulant transformation process on the distribution function to obtain a plurality of cumulants" is re-executed to continuously iterate the fluid dynamic behavior represented by the distribution function.

6. A lattice Boltzmann device based on an entropy-optimized relaxation model, characterized in that: include: an acquisition unit, configured to acquire a distribution function before the collision, and perform a cumulant transformation process on the distribution function to obtain a plurality of cumulants, wherein the plurality of cumulants include a high-order cumulant and a low-order cumulant; The optimization unit is used to maximize the local entropy value of the high-order cumulant by adopting an entropy optimization processing method to obtain an optimized high-order cumulant; the local entropy value of the high-order cumulant is maximized by adopting an entropy optimization processing method to obtain an optimized high-order cumulant, including: The first formula is used to maximize the local entropy value of the high-order cumulant to obtain an optimized high-order cumulant, and the first formula is: ,in, is the optimized high-order cumulant, the high-order cumulant after entropy optimization; is the identity matrix, used for addition of matrix operations; is a coefficient matrix used to modify the calculation of the cumulant; D is a diagonal matrix consisting of the identity matrix and the zero matrix, used to select a specific cumulant part; Represents the grid weight, which is used to measure the weights of different distribution functions; The transformation matrix representing the higher-order cumulants is used to relate the distribution function to the higher-order cumulants; The transformation matrix representing the low-order cumulants is used to relate the distribution function to the low-order cumulants; It is the low-order cumulant. The low-order part obtained by cumulant transformation is used to calculate the high-order cumulant during the optimization process. The calculation results for correcting the higher-order cumulants are obtained from the following relationship: ; The transformation matrix T is used to convert the distribution function into the central moment and can be decomposed into: ; A processing unit, configured to perform inverse transformation processing on the low-order cumulants and the optimized high-order cumulants using an inverse cumulant transformation formula to obtain a distribution function after collision; A migration unit is used to migrate the distribution function after the collision in the physical space and update the distribution function of each grid point. After migrating the distribution function after the collision in the physical space and updating the distribution function of each grid point, it also includes at each time step, first migrating the distribution function after the collision to the adjacent grid point to simulate the movement of fluid microscopic particles so that the fluid state changes in space.

7. A computer device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, 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 5 are implemented.

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