Method and system for constructing convective reaction diffusion model under near-field dynamics framework

Abstract

The invention belongs to the technical field of near field dynamics, and discloses a method and a system for constructing a convection-reaction-diffusion (ARD) model under a near field dynamics framework. According to the method, a PD-ARD equation suitable for the non-uniform flow condition is firstly provided, and the problem that in the prior art, the ARD problem in a complex flow field is not accurately described is effectively solved. In order to realize more accurate coupling calculation, under a near field dynamics (PD) framework, a PD control equation is adopted to solve a velocity field of fluid, and through coupling of a PD equation of viscous flow and a PD-ARD equation under non-uniform flow, an overall model is formed. The method can accurately simulate the convection-diffusion-reaction problem under the viscous flow condition, is suitable for complex environment modeling of multi-scale and multi-physical field coupling, and is widely applied to the fields of industrial design, environment monitoring, scientific research and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of peridynamics, and in particular to a method and system for constructing a convection reaction diffusion model under the framework of peridynamics. Background Art

[0002] Convection-reaction-diffusion (ARD) processes are common in various systems, such as the transport of drugs in the human body, the diffusion of pollutants in groundwater, and the spread of infectious diseases in complex networks. Although some special cases of the classical ARD equation have analytical solutions, most problems need to be solved using numerical approximations. However, there are two major limitations of the classical model of the ARD problem. First, the classical model of the steady-state ARD problem has difficulty in accurately tracking the interface changes in complex situations. Although phase field models can solve this problem, they usually rely on predefined assumptions about the interface change process. Second, the classical ARD equation does not take into account more general long-range interactions (such as anomalous diffusion observed in heterogeneous environments, long-range inhibition in biological pattern formation, etc.).

[0003] Peridynamics (PD) is a non-local theory that introduces the concept of "horizon" and replaces spatial derivatives with integral operators. It does not require the smoothness of the unknown function, so it is very suitable for dealing with spontaneous changes at continuous points. In addition, PD can also solve the singularity problems caused by point contact and separation of materials in classical theory. Therefore, the PD method effectively makes up for the two shortcomings of the classical ARD model. First, the PD framework can naturally handle the interface change process and can accurately predict it without relying on prior assumptions. Secondly, as a non-local method, PD can naturally deal with behaviors with long-range effects. However, the current models for simulating ARD problems in the PD framework are limited to the conditions of uniform flow velocity, but the physical scenario is generally under non-uniform flow fields.

[0004] 1. It is difficult to deal with the phase change problem in the existing technology

[0005] When dealing with phase change problems, traditional convection-reaction-diffusion models either find it difficult to capture the actual phase change process or require the pre-set laws of the phase change process.

[0006] 2. The existing model has low calculation accuracy and insufficient numerical stability

[0007] Existing numerical solution methods are prone to numerical oscillation when dealing with viscous flow, reaction diffusion and material transfer, especially in high gradient areas, resulting in unstable calculation results and large errors.

[0008] 3. Difficulty in coupling reaction dynamics and fluid field in existing technologies

[0009] Under complex fluid motion, material diffusion and chemical reaction rates are difficult to dynamically couple with the fluid field, and traditional models cannot effectively describe the material transfer and transformation process.

[0010] 4. The problem of poor intuitiveness and real-time performance of the existing technology output results

[0011] The calculation results of existing models are mainly presented in the form of numerical data, lacking intuitive data visualization methods and insufficient real-time monitoring capabilities, making it difficult to meet the needs of actual engineering applications. Summary of the invention

[0012] In view of the problems existing in the prior art, the present invention provides a method for constructing a model of convection reaction diffusion in the framework of peridynamics. The present invention effectively solves the technical problems in the prior art, such as the difficulty in handling phase change problems, low calculation accuracy, difficulty in coupling reaction diffusion with fluid fields, and insufficient intuitiveness of the results. Through the system architecture combining software and hardware, the calculation accuracy, numerical stability, data visualization effect and real-time application capability of the convection reaction diffusion model are significantly improved.

[0013] The present invention is implemented as follows: a method for constructing a convection reaction diffusion model under a peridynamics framework comprises:

[0014] Step 1, initialization;

[0015] Initialize velocity, pressure, density, and concentration fields;

[0016] Step 2, viscous flow solution;

[0017] Step 3, solution of solid dissolution / bimolecular reaction.

[0018] Further, the solution of the solid dissolution / bimolecular reaction includes:

[0019] The advection term in the PD-ARD equation is replaced by the PD continuity equation in the medium Euler form, resulting in the following equation:

[0020]

[0021] Where C p (x, t) represents the concentration of substance p at material point x at time t; represents the near field of x; represents other nodes in the near field of x;

[0022] In the PD model, each material point x∈Ω interacts with other points in its near field, which is usually a circle with a radius of δ in two dimensions; yes The area covered; the velocity of the material point x at time t is represented by v(x,t), and is x to A unit vector in the direction of ;

[0023] R pq (x, t) represents the reaction rate between substances p and q; substance p and M p The substances react, which can be expressed as q∈[1,M p ];

[0024] Depending on the role of the substance in a particular reaction, the corresponding reaction rate can be positive or negative; the alpha constant establishes the connection between macroscopic and microscopic speeds, and its value is equal to the dimension;

[0025] The speed in The projection in the direction is defined as For the microscopic diffusion function For example, the relationship between the macroscopic diffusion coefficient and the microscopic diffusion coefficient is definite;

[0026] The two common forms of this function are "constant form" and "trigonometric form", which are: and

[0027] According to the matching between the PD model and the classical model when the concentration distribution of substances in the solution is linear, it can be concluded that in the two-dimensional case, d0 = 4D / πδ 2 and d1=12D / πδ 2 , where D is the diffusion coefficient; in formula (1), set

[0028] For the advection part in formula (1), three schemes are considered: the center scheme, the upwind scheme and the downwind scheme. The center scheme has higher accuracy than the upwind scheme, but its numerical stability is not as good as that of the upwind scheme. The characteristics of the downwind scheme are similar to those of the upwind scheme. The advection term in formula (2) adopts a hybrid scheme, which combines the center scheme and the downwind scheme as follows:

[0029]

[0030] in β is the coefficient connecting the macroscopic velocity and the microscopic velocity in the downwind scheme, which is regarded as a constant; when the flow field is uniform, the PD-ARD equation is compared to obtain β = 2α; here w = 0.8;

[0031] The PD-ARD equation for non-uniform flow has been established;

[0032] Furthermore, the viscous flow solving module:

[0033] The PD control equation of viscous flow will have numerical oscillation. The present invention adds a density diffusion term to the mass conservation equation to weaken this phenomenon:

[0034]

[0035] In the formula, The abbreviation is It is the material point The density at time t, It is the material point is the pressure at time t, b is the volume force at material point x at time t; μ is the fluid viscosity; α p is a constant whose value is equal to the dimension; α μ The value of is determined by a simple flow problem to ensure the linear consistency of the formula. For the 2D case, α μ =16 / 3; η is the correction factor, usually set to 0.1, is a density-dependent microdiffusion function, and the magnitude of the diffusion coefficient is D ρ =c0δ; similar to the above, There are also two types: "Constant" and "Triangular"; to ensure consistency with the previous micro coefficients, set For "constant type"

[0036] The PD governing equations for viscous flow include a pressure field, but the model lacks an explicit equation; for incompressible Newtonian fluids, it is difficult to directly solve the original incompressible equation; an artificial state equation is used to express the pressure as an algebraic function of density:

[0037]

[0038] Among them, ρ0 is the initial density, ρ * is the predicted density of the current step, γ is the material constant, and the material constant of water is 7; c0 is the artificial sound speed; the artificial sound speed will affect the selection of the time step; the higher the artificial sound speed, the smaller the time step, but the more stable the value; in general, the artificial sound speed is set to 10 times the maximum speed of the flow field to ensure that the Mach number M = v / c0 is less than 0.1, so as to ensure that the density change is less than 1% of the initial density;

[0039] Therefore, we first use equation (3-5) to obtain the velocity field, and then substitute the velocity field into equation (1) to solve the ARD process.

[0040] Another object of the present invention is to provide a model building system for convection reaction diffusion under the peridynamics framework, comprising:

[0041] Initialization module, used to initialize velocity, pressure, density and concentration fields;

[0042] Viscous flow solving module, used to solve viscous flow;

[0043] Solid dissolution / bimolecular reaction solving module is used to solve solid dissolution / bimolecular reactions.

[0044] Another object of the present invention is to provide a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method for constructing a convection reaction diffusion model under the framework of peridynamics.

[0045] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to perform the steps of the method for constructing a convection reaction diffusion model under the framework of peridynamics.

[0046] Another object of the present invention is to provide an information data processing terminal, which is used to implement the model building system of convection reaction diffusion under the framework of peridynamics.

[0047] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0048] First, the present invention first proposes the PD-ARD equation under non-uniform flow, which can solve the problems of the prior art. For the convenience of coupling, the velocity field is obtained under the PD framework. Therefore, the present invention couples the PD control equation of viscous flow with the PD-ARD equation under non-uniform flow to obtain an ARD problem that can simulate viscous flow.

[0049] The present invention proposes a method for constructing a convection-reaction-diffusion model under the framework of peridynamics. By introducing dynamic initialization and refined solution processes, the problem of insufficient description of the evolution of complex flow fields and concentration fields in existing peridynamic models is solved. By coupling the solution of viscous flow with the dissolution / reaction process, the interaction between fluid motion and chemical reaction is accurately captured. In addition, the present invention adopts an iterative algorithm to achieve stable calculation of non-uniform initial conditions and complex boundary conditions, significantly improving the stability and accuracy of numerical simulation.

[0050] The present invention has significant technological advances in industrial applications: (1) It realizes high-precision dynamic simulation of fluid flow and chemical reaction processes, which is suitable for material transfer and reaction research in the fields of power transmission and transformation engineering, environmental monitoring, chemical engineering design, etc.; (2) By coupling convection, diffusion and reaction processes, it improves the ability to describe complex multi-scale problems, providing a new tool for optimizing industrial production processes.

[0051] The present invention solves the technical bottleneck of traditional models in dealing with complex convection-reaction-diffusion problems, and provides a more efficient and reliable analysis tool for industry and scientific research. Its application not only promotes technological progress in the fields of chemical industry, energy, environment, etc., but also lays a theoretical foundation for intelligent industrial design and efficient resource utilization. At the same time, the modular design method of the present invention is easy to integrate with existing industrial software or systems, and has broad application prospects and economic benefits.

[0052] Second, the technical solution of the present invention fills the technical gap in the industry at home and abroad:

[0053] Although there are many models that can describe the ARD process at home and abroad, most of them are derived under the framework of classical mechanics, and few studies on the ARD process are conducted under the framework of peridynamics. At the same time, the few models that describe the ARD process under the framework of peridynamics are also limited to uniform flow conditions. The technical solution of the present invention proposes a model that can simulate the ARD process under non-uniform flow conditions under the framework of peridynamics.

[0054] The technical solution of the present invention solves a technical problem that people have been eager to solve but have never succeeded in solving: although the traditional partial differential equation model is used to numerically solve the flow of one-dimensional bimolecular reaction transport flow in isotropic uniform media and compare it with experimental results. However, these types of models, when extended to higher dimensions and applied to complex fields, are difficult to track the evolving interface. Although the phase field model of the reaction-diffusion problem has greater flexibility in tracking the changing interface, it still has to adopt preset functional changes at the interface, which usually does not correspond to the actual physics / chemistry. In contrast, the damage or phase change model based on peridynamics does not have this limitation and has been proven to accurately predict the evolution of the moving interface. However, the model for simulating the ARD process under the peridynamic framework is limited to uniform flow conditions. Here, the present invention introduces a new PD model for transient ARD problems that is universal under non-uniform flow conditions to solve the above problems.

[0055] Third, most of the current models of convection-diffusion-reaction systems rely on the framework of classical mechanics, but lack sufficient accuracy when dealing with phase change problems in the strong coupling of material transfer, fluid dynamics and chemical reactions in multidimensional situations. This limitation makes it difficult to effectively predict microscopic dynamic behaviors and macroscopic effects in industrial application scenarios with complex multi-physical field interactions (such as solute diffusion, solid dissolution, chemical reaction kinetics, etc.). In addition, traditional methods are difficult to capture some non-local behaviors, such as heterogeneous diffusion behavior in heterogeneous environments, long-range inhibition behavior in the differentiation and growth of biological cells, etc. Finally, the existing ARD model under the framework of peridynamics is difficult to describe the ARD process under non-uniform flow rate. Based on the peridynamic framework, the present invention provides a model construction method that is more suitable for phase change processes, non-local effects and multi-physical field coupling. Under this framework, the model can more accurately simulate the flow characteristics, solute diffusion behavior and chemical reaction rate of the fluid when there is a phase change process in the ARD process by introducing the dynamic description of peridynamics. At the same time, combined with the convection, diffusion and reaction equations, the non-local behaviors that are difficult to resolve in traditional methods are included in the solution range, thereby making up for the shortcomings of the existing models. Finally, this model is built in the framework of peridynamics and can describe the ARD process under non-uniform flow rate.

[0056] The present invention has shown significant technological progress in industrial applications in many fields. For example, in the chemical industry, the rate of solid dissolution and the distribution of reactant concentrations in the reactor can be more accurately predicted, providing support for improving reaction efficiency and saving raw material costs; in environmental engineering, it can be used to simulate the diffusion and degradation behavior of pollutants and optimize water purification processes; in the pharmaceutical industry, it can accurately simulate drug release and diffusion processes, providing technical support for drug design and formulation development. By accurately modeling these complex processes, the present invention provides an important basis for improving industrial production efficiency and optimizing process design.

[0057] This paper proposes a complete method system from initialization to fluid dynamics solution to solid dissolution / chemical reaction simulation by making efficient use of the peridynamics framework. Compared with traditional models, the accuracy and stability of solutions in complex situations are significantly improved. This systematic approach provides a comprehensive solution for the research and application of complex convection-diffusion-reaction systems, fills the technical gap in coupled calculations in the microscale and macroscopic fields, and promotes the innovative development of related industries. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a flow chart of a method for constructing a convection reaction diffusion model in a peridynamics framework provided by an embodiment of the present invention.

[0059] Figure 2It is a structural block diagram of a convection reaction diffusion model building system in a peridynamics framework provided by an embodiment of the present invention.

[0060] Figure 3 It is a calculation flow chart of the PD-ARD model of viscous flow in bimolecular reactions and solid dissolution provided by an embodiment of the present invention.

[0061] Figure 4 It is an interaction diagram between a material point provided by an embodiment of the present invention and other material points in its near field.

[0062] Figure 5 It is a diagram of the central format, reverse-wind format and forward-wind format provided by the embodiment of the present invention.

[0063] Figure 6 It is a diagram of initial conditions and boundary conditions of a numerical verification example provided in an embodiment of the present invention.

[0064] Figure 7 It is a cloud diagram of the x-direction velocity of the PD solution and the COMSOL solution in a homogeneous medium example provided by an embodiment of the present invention.

[0065] Figure 8 It is a velocity comparison diagram of the PD solution and the COMSOL solution of the cylinder flow example provided in the embodiment of the present invention.

[0066] Fig. 9 It is a comparison diagram of the concentration of product AB in a homogeneous medium by the PD-ARD model and COMSOL provided in an embodiment of the present invention.

[0067] Fig.10 It is a comparison diagram of the concentration of each substance obtained by PD COMSOL along the horizontal line at 200s (a) and 500s (b) in a calculation example of a homogeneous medium provided by an embodiment of the present invention.

[0068] Fig.11 It is a comparison diagram of AB concentrations obtained in the flow around a cylinder by the PD-ARD model and COMSOL provided in an embodiment of the present invention.

[0069] Fig.12 It is a comparison of the concentrations of substance AB obtained along the horizontal line by PD and COMSOL in the ARD example of flow around a cylinder provided by an embodiment of the present invention. It is a flow diagram around a cylinder by an ARD example.

[0070] Fig.13 1 and 2 are three groups of graphs (a), (b) and (c) provided in an embodiment of the present invention, respectively representing the dissolution of solid A at .

[0071] Fig.143 is a graph of the concentration distribution of the dissolved product AB at 75 s for different Reynolds numbers provided by an embodiment of the present invention (wherein it represents the concentration of the node AB normalized by the saturation concentration of AB).

[0072] Fig.15 Graphs showing the dissolution rates on the left and right sides of a cylinder under three conditions provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0073] 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 embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0074] The convection reaction diffusion model construction system under the framework of peridynamics first obtains the initial state data of the fluid field, concentration field, pressure field and density field through the data acquisition module. Specifically, the system can use satellite remote sensing equipment, laboratory fluid monitoring equipment or high-precision sensors to collect data in real time, covering information such as time evolution and spatial distribution. The collected data is imported into the computing device through the transmission interface to provide accurate and complete initial conditions for subsequent model calculations. In addition, users can input boundary conditions and initial state parameters through a graphical interface to ensure the flexibility and accuracy of model initialization.

[0075] In the data processing module, the system first removes invalid data, and classifies and processes the data according to its characteristics to distinguish different types of fluid field or concentration field information. Subsequently, the system solves the viscous flow, material diffusion and reaction process based on the principle of peridynamics (PD). The PD model calculates the interaction between material points and other points in the near field domain, and accurately describes the motion characteristics of the fluid, the diffusion behavior of the solute and the reaction process by solving the momentum conservation equation, mass conservation equation and reaction-diffusion equation of viscous flow. In this process, numerical calculation algorithms are used to improve calculation accuracy and ensure numerical stability.

[0076] The system performs core numerical calculation tasks through the computing unit, including the collaborative work of the hardware processor and memory. The computing unit couples the solution of the viscous flow field with the material transfer and reaction process, and dynamically updates the fluid field and concentration field. The system gradually optimizes the reconstructed data based on an iterative algorithm and evaluates the reconstruction error (such as the normalized root mean square error NRMSE) at each time step. When the error meets the preset accuracy requirements, the system stops iterating and outputs the final calculation results. This process ensures the accuracy and efficiency of the calculation, and can provide stable solution results even in complex fluid scenarios.

[0077] Finally, the system displays and stores the calculation results through the result output module. The result output module includes a data visualization unit, which can present the evolution of the fluid field and concentration field in the form of dynamic two-dimensional images, so that users can intuitively understand the whole process of fluid movement and reaction diffusion. In addition, the system supports the export of calculation data reports and key parameters, which is convenient for users to conduct further analysis and application. If the user needs real-time monitoring, the system can display the model operation status and update results in real time through the display device to meet the needs of engineering decision-making and scientific research.

[0078] This system realizes the precise construction and efficient solution of the convection-reaction-diffusion model under the framework of near-field dynamics through four core modules: data acquisition, data processing, iterative calculation and result visualization output. It has the advantages of comprehensive data acquisition, high calculation accuracy and intuitive dynamic display.

[0079] like Figure 1 , Figure 3 As shown, a method for constructing a convection reaction diffusion model in a peridynamics framework provided by an embodiment of the present invention includes the following steps:

[0080] S101, initialization;

[0081] Initialize velocity, pressure, density, and concentration fields;

[0082] S102, viscous flow solution;

[0083] S103, Solution of solid dissolution / bimolecular reactions.

[0084] In the framework of peridynamics, the initialization phase aims to establish the computational basis for the model. By defining the initial conditions of the velocity field, pressure field, density field, and concentration field, the initial state of the simulation object is accurately described. These field variables can be obtained through experimental measurements, known boundary conditions, or theoretical calculations. Specifically, the velocity field is used to describe the flow characteristics of the fluid, the pressure field is used to describe the pressure distribution in the fluid, the density field reflects the spatial distribution of substances in the fluid, and the concentration field describes the distribution of solutes or reactants. The accuracy of initialization directly affects the stability and accuracy of subsequent calculations.

[0085] At this stage, the model uses the basic equations of peridynamics (such as the momentum conservation equation and the mass conservation equation) to solve the flow characteristics of viscous fluids. The dynamic behavior of small areas in the fluid is simulated by considering the effects of viscosity, fluid inertia, and external forces (such as gravity or shear force). During the solution process, Gaussian orthogonality is used to approximate the integral terms, and the forward Euler method is selected for the time derivative, and an iterative algorithm is used to obtain a steady-state or transient solution. The solution of viscous flow provides the basis for the transfer of solutes or reactants, while affecting the spatial distribution and speed of solid dissolution or chemical reactions.

[0086] The solution of solid dissolution or bimolecular reaction is based on the convection-reaction-diffusion equation in the peridynamic framework to describe the transfer and transformation behavior of substances. In this process, the convection term reflects the process of solute or reactant moving with the fluid, the diffusion term describes the diffusion of substances due to concentration gradient, and the reaction term describes the rate and mechanism of chemical reactions. The model simulates the dynamic process of solid dissolution rate or chemical reaction and accurately predicts the evolution of concentration field by coupling convection, diffusion and reaction.

[0087] In each time step, the viscous flow solution is coupled with the dissolution / reaction process to achieve dynamic updates of the fluid field and concentration field. Through iterative algorithms, the model can track changes in the fluid-solid interface, the consumption of reactants, and the distribution of products in real time. Ultimately, the model outputs complete flow field and concentration field evolution data, revealing the complex dynamic behavior of the convection-diffusion-reaction system. This process can simulate practical engineering problems with multi-scale and multi-physics field coupling, providing important references for industrial design, environmental monitoring, and scientific research.

[0088] Solution of solid dissolution / bimolecular reaction provided by the embodiment of the present invention:

[0089] The advection term in the PD-ARD equation is replaced by the PD continuity equation in the medium Euler form, resulting in the following equation:

[0090]

[0091] Where C p (x, t) represents the concentration of substance p at material point x at time t; represents the near field of x;

[0092] In the PD model, each material point x∈Ω interacts with other points in its near field, which is usually a circle with a radius of δ in two dimensions; yes The area covered; the velocity of the material point x at time t is represented by v(x,t), and is x to A unit vector in the direction of ;

[0093] R pq (x, t) represents the reaction rate between substances p and q; substance p and M p The substances react, which can be expressed as q∈[1,M p ];

[0094] Depending on the role of the substance in a particular reaction, the corresponding reaction rate can be positive or negative; the alpha constant establishes the connection between macroscopic and microscopic speeds, and its value is equal to the dimension;

[0095] The speed in The projection in the direction is defined as For the microscopic diffusion function For example, the relationship between the macroscopic diffusion coefficient and the microscopic diffusion coefficient is definite;

[0096] The two common forms of this function are "constant form" and "trigonometric form", which are: and

[0097] According to the matching between the PD model and the classical model when the concentration distribution of substances in the solution is linear, it can be concluded that in the two-dimensional case, d0 = 4D / πδ 2 and d1=12D / πδ 2 , where D is the diffusion coefficient; in formula (1), set

[0098] For the advection part in formula (1), three schemes are considered: the center scheme, the upwind scheme and the downwind scheme. The center scheme has higher accuracy than the upwind scheme, but its numerical stability is not as good as that of the upwind scheme. The characteristics of the downwind scheme are similar to those of the upwind scheme. The advection term in formula (2) adopts a hybrid scheme, which combines the center scheme and the downwind scheme as follows:

[0099]

[0100] in β is the coefficient connecting the macroscopic velocity and the microscopic velocity in the downwind scheme, which is regarded as a constant; when the flow field is uniform, the PD-ARD equation is compared to obtain β = 2α; here w = 0.8;

[0101] The PD-ARD equation under non-uniform flow has been established;

[0102] The viscous flow solution provided by the embodiment of the present invention is:

[0103] The PD control equation of viscous flow will have numerical oscillation. The present invention adds a density diffusion term to the mass conservation equation to weaken this phenomenon:

[0104]

[0105] In the formula, The abbreviation is It is the material point The density at time t, It is the material point is the pressure at time t, b is the volume force at material point x at time t; μ is the fluid viscosity; α p is a constant whose value is equal to the dimension; α μThe value of is determined by a simple flow problem to ensure the linear consistency of the formula. For the 2D case, α μ =16 / 3; η is the correction factor, usually set to 0.1, is a density-dependent microdiffusion function, and the magnitude of the diffusion coefficient is D ρ =c0δ; similar to the above, There are also two types: "Constant" and "Triangular"; to ensure consistency with the previous micro coefficients, set For "constant type"

[0106] The PD governing equations for viscous flow include a pressure field, but the model lacks an explicit equation; for incompressible Newtonian fluids, it is difficult to directly solve the original incompressible equation; an artificial state equation is used to express the pressure as an algebraic function of density:

[0107]

[0108] Among them, ρ0 is the initial density, ρ * is the predicted density of the current step, γ is the material constant, and the material constant of water is 7; c0 is the artificial sound speed; the artificial sound speed will affect the selection of the time step; the higher the artificial sound speed, the smaller the time step, but the more stable the value; in general, the artificial sound speed is set to 10 times the maximum speed of the flow field to ensure that the Mach number M = v / c0 is less than 0.1, so as to ensure that the density change is less than 1% of the initial density;

[0109] Therefore, we first use equation (3-5) to obtain the velocity field, and then substitute the velocity field into equation (1) to solve the ARD process.

[0110] like Figure 2 As shown, a model building system for convection reaction diffusion in a peridynamics framework provided by an embodiment of the present invention includes:

[0111] Initialization module, used to initialize velocity, pressure, density and concentration fields;

[0112] Viscous flow solving module, used to solve viscous flow;

[0113] Solid dissolution / bimolecular reaction solving module is used to solve solid dissolution / bimolecular reactions.

[0114] Another object of the present invention is to provide a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method for constructing a convection reaction diffusion model under the framework of peridynamics.

[0115] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to perform the steps of the method for constructing a convection reaction diffusion model under the framework of peridynamics.

[0116] Another object of the present invention is to provide an information data processing terminal, which is used to implement the model building system of convection reaction diffusion under the framework of peridynamics.

[0117] The present invention is specifically implemented:

[0118] The advection term in the PD-ARD equation is replaced by the PD continuity equation in the medium Euler form, and the following equation can be obtained:

[0119]

[0120] like Figure 4 , where C p (x, t) represents the concentration of substance p at material point x at time t; represents the near field of x; in the PD model, each material point x∈Ω interacts with other points in its near field. In two dimensions, the near field is usually a circle with a radius of δ; yes The area covered (area in two dimensions); the velocity of a material point x at time t is denoted by v(x,t), and is x to The unit vector in the direction of R pq (x, t) represents the reaction rate between substances p and q; substance p and M p The substances react, which can be expressed as q∈[1,M p ]; Depending on the role of a substance in a particular reaction (e.g., as a product or reactant), the corresponding reaction rate can be positive or negative; the α constant establishes the connection between macroscopic and microscopic speeds, and its value is equal to the dimension (e.g., α = 2 in two dimensions); the speed is converted to The projection in the direction is defined as For the microscopic diffusion function For the macroscopic diffusion coefficient, the relationship between the macroscopic diffusion coefficient and the microscopic diffusion coefficient is definite; the two common forms of this function are "constant type" and "triangular type", which are: and According to the matching between the PD model and the classical model when the concentration distribution of substances in the solution is linear, it can be concluded that in the two-dimensional case, d0 = 4D / πδ 2 and d1=12D / πδ 2 , where D is the diffusion coefficient; in formula (1), set

[0121] For the advection part in equation (1), three schemes are considered (see Figure 5 ): center scheme, upwind scheme and downwind scheme; the center scheme has higher accuracy than the upwind scheme, but its numerical stability is not as good as that of the upwind scheme; the characteristics of the downwind scheme are similar to those of the upwind scheme; the advection term in formula (2) adopts a hybrid scheme, combining the center scheme and the downwind scheme as follows:

[0122]

[0123] in β is the coefficient connecting the macroscopic velocity and the microscopic velocity in the downwind scheme. For simplicity, it is regarded as a constant. When the flow field is uniform, β = 2α is obtained by comparing with the PD-ARD equation. Here, w = 0.8 is taken.

[0124] So far, the PD-ARD equation under non-uniform flow has been established;

[0125] Since numerical oscillation may occur when using the proposed PD control equation for viscous flow, the present invention adds a density diffusion term to the mass conservation equation to weaken this phenomenon:

[0126]

[0127] In the formula, The abbreviation is It is the material point The density at time t, It is the material point is the pressure at time t, b is the volume force at material point x at time t; μ is the fluid viscosity; α p is a constant whose value is equal to the dimension (since this article discusses two-dimensional cases, α p =2); α μ The value of is determined by a simple flow problem to ensure the linear consistency of the formula. For the 2D case, α μ =16 / 3; η is the correction factor, usually set to 0.1, is a density-dependent microdiffusion function, and the magnitude of the diffusion coefficient is D ρ =c0δ; similar to the above, There are also two types: "Constant" and "Triangular"; to ensure consistency with the previous micro coefficients, set For "constant type"

[0128] The PD equation for viscous fluids contains a pressure field, but the model lacks an explicit equation; for incompressible Newtonian fluids, it is difficult to directly solve the original incompressible equation; so an artificial state equation is used here to express the pressure as an algebraic function of density:

[0129]

[0130] Among them, ρ0 is the initial density, ρ * is the predicted density of the current step, γ is the material constant, and the material constant of water is 7; c0 is the artificial sound speed; the artificial sound speed will affect the selection of the time step; the higher the artificial sound speed, the smaller the time step, but the more stable the value; in general, the artificial sound speed is set to 10 times the maximum speed of the flow field to ensure that the Mach number M = v / c0 is less than 0.1, so as to ensure that the density change is less than 1% of the initial density;

[0131] Therefore, we first obtain the velocity field through equation (3-5), and then bring the velocity field into equation (1) to solve the ARD process;

[0132] Assume that the reaction between the purifier and the pollutant is an irreversible bimolecular reaction A+B→AB. Assume that all substances are water-soluble. Assume that the diffusion coefficient of each substance is equal D=0.0017cm 2 / s. Therefore, formula (1) can be rewritten accordingly:

[0133]

[0134] In the formula, C A , C B and C AB Represents the concentration of substances A, B and AB respectively. AB is the reaction rate of the bimolecular reaction, which is set as R AB =4.1L / (mol·s).

[0135] Consider a two-dimensional ARD problem such as Figure 6 Specifically, Figure 6 (a) describes the purification example without obstacles (ARD problem in homogeneous medium). Figure 6 (b) illustrates a purification example with an obstacle (ARD problem for flow around a cylinder). These examples are used to verify the proposed coupled PD-ARD model for viscous flow. The density of the fluid is ρ = 1000 kg / m 3 , viscosity is μ = 10 -3 kg·m -1 This value is used in all examples. In addition, the artificial sound velocity is set to c0 = 0.01 m / s. The inlet velocity is defined as v0 = 1 × 10 -4m / s, initial concentration C0=0.02mol / L, and the outlet maintains zero pressure.

[0136] Figure 7 and Figure 8 The velocity field convergence results obtained using the modified PD governing equations for viscous flow and COMSOL simulation are presented. The results show that the velocity field predicted by the PD model is in good agreement with the velocity field observed by COMSOL.

[0137] Fig. 9 and Fig.11 The concentration distribution of product AB at different times is shown. It can be seen that the results of the PD model are very consistent with the results of COMSOL. For further analysis, we compared Figure 6 (a) The concentrations of the three substances A, B and AB in PD and COSMOL solutions at the horizontal line y = 0 (see Fig.10 ). Similarly, in Figure 6 In the example shown in (b), the concentrations of three substances A, B and AB in the PD solution and the COSMOL solution at the horizontal line y = 0.015m are compared (see Fig.12 ). This shows that the results of the PD-ARD coupling model under viscous flow are highly consistent with the COMSOL output results.

[0138] consider Figure 6 In the example in (b), the cylinder representing substance A is assumed to be soluble, and the substance dissolved in water is AB. The dissolution process is assumed to be an irreversible chemical reaction: A→AB. The PD-ARD equation governing this process is as follows:

[0139]

[0140] Among them, R A represents the dissolution rate of substance A in the solution. Assume that the dissolution rate is constant at R A =4.2 mol / (L·s). The solid concentration of substance A is C A,soild =100mol / L. Assume that the saturation concentration of AB is C sat =20mol / L. During solid dissolution, once the concentration of AB reaches the saturation concentration, dissolution stops. When the concentration of AB drops below the saturation level, dissolution restarts.

[0141] The diffusion rate of substance AB in the solution is set to D = 1×10 -6 m 2 / s. This example uses Figure 6 (b) The same configuration, the only modification is the solubility of the cylinder and different inlet velocities. Three flow cases are considered, with inlet velocities v0 = 1 × 10 -4m / s,5×10 -4 m / s, 25×10 -4 m / s, and the corresponding Reynolds numbers are Re = 2, 10, and 50. The relevant artificial sound speeds in these cases are c0 = 0.01 m / s, 0.05 m / s, and 0.25 m / s.

[0142] Fig.13 The dissolution of solid substance A at Re = 2, 10, and 50 is shown. As shown in the figure, increasing the Reynolds number not only speeds up the dissolution rate of the cylinder, but also leads to asymmetry in the remaining part of the solid. For example, a higher Reynolds number will enhance the fluid scouring effect on the left side and the upper and lower sides of the cylinder, resulting in faster dissolution in these areas. This left-right asymmetry can be quantified by calculating the amount of substance A on both sides of the cylinder (see Fig.15 ), as shown below: represents half of the sum of the amount of substance A of all nodes in the domain at the initial moment, and n represents the total number of nodes. In addition, and They respectively represent the sum of the amount of material A at all nodes on the left and right sides of the cylinder at time t.

[0143] Further analysis, Fig.14 and Fig.15 It shows that in the initial stage of dissolution, the dissolution rates on the left and right sides of the cylinder are almost the same. This is because at this stage, diffusion mainly affects the dissolution rate, and the diffusion rate remains consistent under the three conditions. However, as the dissolution process proceeds, substance AB will flow from the left to the right. Therefore, at a given Reynolds number, the dissolution rate on the left side of the cylinder always exceeds that on the right side. The higher the Reynolds number, the more obvious this effect is, resulting in more severe asymmetry.

[0144] Example 1: Optimization of efficient reactors in the chemical industry

[0145] In the chemical industry, dissolution, diffusion and reaction processes play a central role in reactor design and optimization. For example, the optimization of dissolution and mass transfer of industrial catalysts requires precise control of reaction conditions to improve production efficiency. The convection reaction diffusion model constructed by the peridynamic framework of the present invention can accurately simulate the coupling relationship between the dissolution of catalyst particles, solute diffusion and reaction rate.

[0146] Specific applications:

[0147] In a multiphase reactor, this model can be used to simulate the concentration distribution, diffusion path and reaction rate of catalyst particles when they are dissolved.

[0148] Optimize the fluid dynamic conditions (such as pressure, temperature and flow rate) within the reactor to maximize reaction efficiency and feedstock conversion.

[0149] Example 2: Diffusion and degradation of water pollutants in environmental engineering

[0150] In the field of environmental protection, the diffusion and degradation process of pollutants in water bodies is the key to designing effective treatment solutions. The present invention can simulate the dynamic behavior of pollutants in flowing water bodies and predict the concentration changes during the degradation process by coupling modeling the diffusion, flow and degradation processes of pollutants.

[0151] Specific applications:

[0152] Regarding the diffusion behavior of harmful chemicals (such as heavy metals or organic pollutants) in rivers, the model can combine water flow velocity and pressure distribution to predict the spatial distribution and diffusion path of pollutant concentrations.

[0153] Combining convection and reaction kinetics, the degradation process of pollutants after the introduction of chemical agents is simulated to optimize the dosage and introduction strategy of the agents.

[0154] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0155] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A system for constructing a convection-reaction-diffusion model in a peridynamic framework, comprising: Data acquisition module: obtains the initial state data of the fluid field, concentration field, pressure field and density field through sensors or experimental equipment, and transmits the data to the computing device; Data processing module: an application running on a computing device that removes invalid data, classifies and processes different types of data, and solves viscous flow, material diffusion, and reaction processes based on peridynamic principles; Computational unit: includes hardware processor and memory, used to execute numerical calculation algorithms, couple fluid motion with material transfer data, dynamically update fluid field and concentration field through iterative algorithms, and evaluate reconstruction errors; Result output module: outputs the calculation results through display devices or storage devices, including the complete flow field, concentration field evolution data, and key parameters during system operation.

2. The system according to claim 1, characterized in that The data acquisition module includes satellite remote sensing equipment, laboratory fluid monitoring equipment or high-precision sensors, which are used to collect spatially distributed and temporally evolving vegetation or fluid related data in real time.

3. The system according to claim 1, characterized in that The data processing module allows the user to input boundary conditions, initial state parameters and calculation accuracy requirements through a graphical interface based on user operations, so as to automatically adjust the parameter settings of the solution model.

4. The system according to claim 1, characterized in that The result output module includes a data visualization unit, which generates a dynamic three-dimensional image of the evolution process of the fluid field and the concentration field in a graphical display form, and supports the export of data reports or real-time monitoring functions.

5. A method for constructing a convection-reaction-diffusion model in a peridynamics framework, characterized in that: The following steps are involved: Step 1, initialization: Initialize the velocity field, pressure field, density field and concentration field in the model, determine the initial state through experimental measurement, boundary conditions or theoretical calculation, and provide a basis for subsequent calculations; Step 2, viscous flow solution: Based on the basic equations of peridynamics, including the momentum conservation equation and the mass conservation equation, combined with the viscosity effect, fluid inertia and external force, the flow characteristics of the fluid are solved using numerical methods and the viscous flow field is generated; Step 3, solution of solid dissolution / bimolecular reaction: Based on the convection-diffusion equation, combined with the reaction kinetics equation, a material transfer and transformation model is established, in which the convection term describes the behavior of the solute moving with the fluid, the diffusion term describes the material diffusion process caused by the concentration gradient, and the reaction term describes the rate and mechanism of the chemical reaction; Step 4, comprehensive calculation and iterative solution: Based on each time step, the solution results of the viscous flow are coupled with the solution results of the dissolution / reaction process, and the fluid field and concentration field are dynamically updated through an iterative algorithm, and finally the complete flow field and concentration field evolution data are output.

6. The method for constructing a convection-reaction-diffusion model in the peridynamics framework as claimed in claim 5, characterized in that: The solution of the solid dissolution / bimolecular reaction includes: The advection term in the PD-ARD equation is replaced by the PD continuity equation in the medium Euler form, resulting in the following equation: Where C p (x, t) represents the concentration of substance p at material point x at time t; represents the near field of x; In the PD model, each material point x∈Ω interacts with other points in its near field, which is usually a circle with a radius of δ in two dimensions; yes The area covered; the velocity of the material point x at time t is represented by v(x,t), and is x to A unit vector in the direction of ; R pq (x, t) represents the reaction rate between substances p and q; substance p and M p The substances react, which can be expressed as q∈[1,M p ]; Depending on the role of the substance in a particular reaction, the corresponding reaction rate can be positive or negative; the alpha constant establishes the connection between macroscopic and microscopic speeds, and its value is equal to the dimension; The speed in The projection in the direction is defined as For the microscopic diffusion function For example, the relationship between the macroscopic diffusion coefficient and the microscopic diffusion coefficient is definite; The two common forms of this function are "constant form" and "trigonometric form", which are: and According to the matching between the PD model and the classical model when the concentration distribution of substances in the solution is linear, it can be concluded that in the two-dimensional case, d0 = 4D / πδ 2 and d1=12D / πδ 2 , where D is the diffusion coefficient; in formula (1), set For the advection part in formula (1), three schemes are considered: the center scheme, the upwind scheme and the downwind scheme. The center scheme has higher accuracy than the upwind scheme, but its numerical stability is not as good as that of the upwind scheme. The characteristics of the downwind scheme are similar to those of the upwind scheme. The advection term in formula (2) adopts a hybrid scheme, which combines the center scheme and the downwind scheme as follows: in β is the coefficient connecting the macroscopic velocity and the microscopic velocity in the downwind scheme, which is regarded as a constant; when the flow field is uniform, the PD-ARD equation is compared to obtain β = 2α; here w = 0.8; The PD-ARD equation for non-uniform flow has been established; The PD control equation of viscous flow will have numerical oscillation. The present invention adds a density diffusion term to the mass conservation equation to weaken this phenomenon: In the formula, The abbreviation is It is the material point The density at time t, It is the material point is the pressure at time t, b is the volume force at material point x at time t; μ is the fluid viscosity; α p is a constant whose value is equal to the dimension; α μ The value of is determined by a simple flow problem to ensure the linear consistency of the formula. For the 2D case, α μ =16 / 3; η is the correction factor, usually set to 0.1, is a density-dependent microdiffusion function, and the magnitude of the diffusion coefficient is D ρ =c0δ; similar to the above, There are also two types: "Constant" and "Triangular"; to ensure consistency with the previous micro coefficients, set "Constant type" 7. The method for constructing a convection-reaction-diffusion model in the peridynamics framework as claimed in claim 6, characterized in that: The PD equation for viscous flow contains a pressure field, but the model lacks an explicit equation; for incompressible Newtonian fluids, it is difficult to directly solve the original incompressible equation; an artificial state equation is used to express the pressure as an algebraic function of density: Among them, ρ0 is the initial density, ρ * is the predicted density of the current step, γ is the material constant, and the material constant of water is 7; c0 is the artificial sound speed; the artificial sound speed will affect the selection of the time step; the higher the artificial sound speed, the smaller the time step, but the more stable the value; in general, the artificial sound speed is set to 10 times the maximum speed of the flow field to ensure that the Mach number M = v / c0 is less than 0.1, so as to ensure that the density change is less than 1% of the initial density; Therefore, we first use equation (3-5) to obtain the velocity field, and then substitute the velocity field into equation (1) to solve the ARD process.

8. A system for constructing a convection reaction diffusion model under a peridynamics framework, which implements the method for constructing a convection reaction diffusion model under a peridynamics framework as claimed in any one of claims 5 to 7, characterized in that: The convection reaction diffusion model building system in the peridynamics framework includes: Initialization module, used to initialize velocity, pressure, density and concentration fields; Viscous flow solving module, used to solve viscous flow; Solid dissolution / bimolecular reaction solving module is used to solve solid dissolution / bimolecular reactions.

9. A computer device, characterized in that: The computer device includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method for constructing a convection reaction diffusion model under the peridynamics framework as described in any one of claims 5 to 7.

10. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the method for constructing a convection reaction diffusion model under the framework of peridynamics as claimed in any one of claims 5 to 7.

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