Sodium-ion battery multi-scale simulation method based on adaptive grid division

Abstract

The invention discloses a sodium ion battery multi-scale simulation method based on adaptive grid division, and relates to the technical field of electrochemical energy storage system simulation, and the method comprises the steps: building a sodium ion battery multi-scale simulation model comprising a micro-scale model, a mesoscale model and a macro-scale model; transmitting a diffusion coefficient output by the micro-scale model to a mesoscale model based on a preset cross-scale parameter transmission channel, obtaining a transmission parameter by simulating ion transmission in an electrode, transmitting the transmission parameter to a macro-scale model, and performing multi-physical field coupling simulation of the sodium ion battery; wherein in the multi-physical field coupling simulation process of the sodium ion battery by the macroscale model, the physical field distribution state is monitored in real time, and adaptive grid division is executed based on the physical field distribution state. According to the method, the calculation amount in the simulation process can be reduced, and the simulation precision of the core area is guaranteed.

Description

Technical Field

[0001] This invention relates to the field of electrochemical energy storage system simulation technology, and in particular to a multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation. Background Technology

[0002] Energy storage technology has become a core support for the development of the new energy industry. Sodium-ion batteries, with their advantages of abundant resources, low cost, and excellent safety performance, have shown broad application prospects in large-scale energy storage, portable electronic devices, and other fields. Currently, the research and development of sodium-ion batteries is accelerating from material screening to device performance optimization and industrialization. Computer simulation technology, as a key means to shorten the research and development cycle and reduce testing costs, has become a core tool for battery design and performance prediction.

[0003] In existing sodium-ion battery simulation models, from a scale perspective, microscopic models reveal the sodium-ion diffusion mechanism through molecular dynamics simulations, but their computational complexity is extremely high, with single-condition simulations taking several days, making it difficult to support multi-parameter optimization and system-level analysis. While macroscopic models can achieve efficient simulations of system-level thermal management scenarios, their insufficient accuracy due to neglecting the crucial influence of material microstructure on ion transport and reaction kinetics results in inaccurate simulation performance, failing to accurately reflect the actual battery performance. Furthermore, in macroscopic-scale multiphysics coupled simulations, traditional fixed-mesh methods exacerbate this situation: fine meshes are required to ensure simulation accuracy in high-gradient regions, but this leads to a severe waste of computational resources in uniform regions, with computational load increasing exponentially and simulation efficiency significantly reduced. If coarse meshes are used to balance efficiency, it becomes difficult to identify the physical details of key regions, further amplifying errors in cross-scale parameter transfer, ultimately resulting in excessive deviations between simulation results and actual performance. Moreover, this problem is more pronounced in large-scale energy storage system simulations, where it is difficult to balance accuracy and efficiency in battery simulation. Summary of the Invention

[0004] To address the problem of balancing simulation accuracy and efficiency in existing battery simulation models, this invention provides a multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation, which can reduce computational load while ensuring simulation accuracy in core regions. The specific technical solution is as follows: This invention provides a multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation, comprising: Establish a multi-scale simulation model for sodium-ion batteries, including microscale, mesoscale, and macroscale models; Based on the preset cross-scale parameter transfer channel, the diffusion coefficient output by the microscale model is transferred to the mesoscale model. The transfer parameters are obtained by simulating ion transport within the electrode. The transfer parameters are then transferred to the macroscale model to perform multi-physics coupling simulation of sodium-ion batteries. In the process of multi-physics coupling simulation of sodium-ion batteries in the macro-scale model, the physical field distribution is monitored in real time, and adaptive mesh generation is performed based on the physical field distribution.

[0005] Preferably, the establishment of a multi-scale simulation model for sodium-ion batteries, including microscale models, mesoscale models, and macroscale models, includes: The microscale model was constructed, and the diffusion barrier of sodium ions in hard carbon anode material was calculated using density functional theory. The diffusion barrier was then converted into the diffusion coefficient. The mesoscale model is constructed based on the pore network model of the electrode microstructure, and the lattice Boltzmann method is used to simulate the transport process of electrolyte and sodium ions in the pore network model, and the transport parameters are obtained, wherein the diffusion coefficient output by the microscale model is used as the input parameter. The macroscopic-scale model is constructed by establishing a multiphysics coupling model that integrates electrochemical field, temperature field and structural stress field based on multiphysics coupling simulation. This model is used to simulate the external characteristics and internal state of the battery during charging and discharging. The output parameters of the mesoscopic-scale model are imported into the multiphysics coupling model.

[0006] Preferably, during the simulation of the macroscopic model, real-time monitoring of the physical field distribution and adaptive mesh generation based on the physical field distribution include: During the simulation of the macroscopic model, the temperature and concentration gradients of each region are calculated in real time. If the temperature and / or sodium ion concentration gradient in each region is higher than the corresponding preset grid threshold, the grid of that region will be finer; otherwise, the grid of that region will be coarser.

[0007] Preferably, the real-time monitoring of the physical field distribution state and the adaptive meshing based on the physical field distribution state further includes: The physical quantity gradients in the simulation process are scanned at preset time intervals, and mesh merging is performed on regions where the gradient value is lower than the preset coarsening threshold.

[0008] Preferably, the simulation process of the macroscopic scale model further includes: To suit different physical field characteristics, a suitable mesh type is selected. The electrochemical field uses a structured mesh, while the mechanical force field uses an unstructured mesh. Real-time data interaction between meshes is achieved through overlapping meshes.

[0009] Preferably, the conversion formula for converting the diffusion barrier criterion to the diffusion coefficient is as follows: Among them, E a D is the diffusion barrier; D is the diffusion coefficient; is the pre-exponential factor; R is the universal gas constant; T is the absolute temperature.

[0010] Preferably, the preset cross-scale parameter transmission channel is a bidirectional feedback channel; After the macroscopic model completes the multiphysics coupling simulation, the average electrode current density and temperature field distribution obtained from the macroscopic model simulation are fed back to the microscopic model to correct the boundary conditions and temperature parameters in the density functional theory calculation in the microscopic model, and to recalculate the diffusion barrier and iteratively update the diffusion coefficient.

[0011] Preferably, the preset grid threshold is adjusted based on the real-time charge / discharge state of the battery: During the constant current charging stage, the first set of encryption thresholds is used; during the constant voltage charging stage, the second set of encryption thresholds is used; the first set of encryption thresholds is lower than the second set of encryption thresholds.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention presents a multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation. It extracts the sodium-ion diffusion barrier from a microscale model and converts it into the diffusion coefficient. A mesoscale model then simulates ion transport within the electrodes to obtain key transport parameters, ensuring the microscopic correlation of macroscopic simulation input parameters. This overcomes the shortcomings of traditional macroscopic models that neglect the microstructure of materials, improving simulation accuracy and enabling simulation results to more accurately reflect the actual performance of the battery. Simultaneously, the adaptive mesh generation can respond to the distribution of macroscopic physical fields in real time. This not only avoids the waste and inefficiency caused by fixed fine meshes but also solves the problem of fixed coarse meshes failing to identify key details, reducing computational load while ensuring simulation accuracy in core areas. By combining the orderly transfer of parameters across scales with the dynamic adaptation of the adaptive mesh, the scale transition error is effectively reduced, enabling real-time response in the simulation of large-scale energy storage systems. Attached Figure Description

[0013] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0014] Figure 1This is a flowchart of the multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation, as described in this invention.

[0015] Figure 2 This is a flowchart illustrating the construction process of the multi-scale simulation model of the present invention.

[0016] Figure 3 This is a schematic diagram of the multi-scale simulation model architecture of the present invention.

[0017] Figure 4 This is a flowchart of the adaptive mesh generation process of the present invention.

[0018] Figure 5 This is a comparison chart of the adaptive mesh division effect of the present invention.

[0019] Figure 6 This is a flowchart illustrating the iterative optimization process for cross-scale parameter transfer in this invention.

[0020] Figure 7 This is a flowchart of the grid encryption threshold adjustment process of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] It should be understood that, when used in this specification, the terms “comprising” and “including” indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0023] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0024] It should also be further understood that the term "and / or" as used in this specification refers to any combination of one or more of the associated listed items, as well as all possible combinations, and includes such combinations.

[0025] Please refer to the following examples. Figures 1 to 7 .

[0026] This invention provides a multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation, comprising: Establish a multi-scale simulation model for sodium-ion batteries, including microscale, mesoscale, and macroscale models; Based on the preset cross-scale parameter transfer channel, the diffusion coefficient output by the microscale model is transferred to the mesoscale model. The transfer parameters are obtained by simulating ion transport within the electrode. The transfer parameters are then transferred to the macroscale model to perform multi-physics coupling simulation of sodium-ion batteries. like Figure 3 The diagram shows the architecture of a multi-scale simulation model, as follows: Figure 2 The process of constructing a multi-scale simulation model is as follows: The microscale model was constructed, and the diffusion barrier of sodium ions in the hard carbon anode material was calculated using density functional theory. The diffusion barrier was then converted into the diffusion coefficient of sodium ions. By establishing a crystalline or amorphous structure model of hard carbon, including atomic coordinates and lattice parameters, the migration path of sodium ions in hard carbon is calculated using DFT to find transition states and energy barriers. Alternatively, a transition state search method can be used to calculate the migration path of sodium ions in hard carbon and determine the transition states and energy barriers.

[0027] Diffusion barrier The calculation formula is: in, It is the transition state energy. It is the initial state energy.

[0028] Diffusion barrier Converting to diffusion coefficient, the diffusion barrier is converted to the diffusion coefficient using the Arrhenius formula. : in, It refers to the pre-factor, which is determined through experimental or theoretical fitting; It is the universal gas constant; It is absolute temperature.

[0029] The calculated diffusion coefficient As output, it is passed to the mesoscale model.

[0030] The mesoscale model is constructed based on the pore network model of the electrode microstructure, and the lattice Boltzmann method is used to simulate the transport process of electrolyte and sodium ions in the pore network model, and the transport parameters are obtained, wherein the diffusion coefficient output by the microscale model is used as the input parameter. A pore network model is constructed by obtaining the three-dimensional microstructure of the electrode from experimental data, and generating a pore network model including pore size distribution, connectivity, and topology.

[0031] The microstructure is discretized into a regular grid, with each grid cell representing a pore or solid phase. The diffusion coefficient is output at the microscale. As input parameters, they define the diffusion behavior of ions in the electrolyte. The Lattice Boltzmann method (LBM) simulation uses the Discrete Boltzmann equation, whose basic form is: in, It is the direction of the particle Distribution function on; It is a position vector; It is a discrete velocity vector; It is the time step; It is a collision operator, usually using the BGK model: in, It is the relaxation time, which is related to the diffusion coefficient; It is the equilibrium distribution function.

[0032] Macroscopic physical quantities are obtained by iteratively solving the distribution function. The effective diffusion coefficient is then calculated from the LBM simulation results. Penetration rate Transmission parameters, etc.

[0033] Effective diffusion coefficient By fitting Fick's law, we obtain: in, It is ion flux. It refers to ion concentration.

[0034] Penetration Calculated using Darcy's law: in, It's the flow rate. It's viscosity. It's pressure.

[0035] Transmit parameters , This is then passed to the macroscopic scale model.

[0036] The macroscopic-scale model is constructed by establishing a multiphysics coupling model that integrates electrochemical field, temperature field and structural stress field based on multiphysics coupling simulation. This model is used to simulate the external characteristics and internal state of the battery during charging and discharging. The output parameters of the mesoscopic-scale model are imported into the multiphysics coupling model.

[0037] Constructing multiphysics coupling equations: The electrochemical field describes the sodium ion concentration distribution and potential distribution using the following equation: in, It refers to the sodium ion concentration; It is the effective diffusion coefficient of the mesoscale output; It is the current density; It is Faraday's constant.

[0038] The temperature field describes the temperature distribution and uses the energy conservation equation: in, It is density; It is specific heat capacity; It is thermal conductivity; It is the heat generation rate, including Joule heat and reaction heat.

[0039] The structural stress field describes the distribution of mechanical stress using equilibrium equations: Among them, stress tensor With strain Related, through the constitutive equation: in, It is the elastic tensor, strain Calculation of volume change caused by concentration change.

[0040] Partial differential equations are discretized using the finite element method or finite volume method, and multiphysics problems are solved using an iterative coupling strategy. The macroscopic model is initialized using the transmission parameters output at the mesoscopic scale as input.

[0041] In the process of multi-physics coupling simulation of sodium-ion batteries in the macro-scale model, the physical field distribution is monitored in real time, and adaptive mesh generation is performed based on the physical field distribution.

[0042] Real-time monitoring of physical field distribution, at each time step Calculate the physical quantity gradients in each grid region, including the temperature gradient. and sodium ion concentration gradient The gradient calculation employs a numerical method.

[0043] Preset temperature gradient threshold (Unit: K / m); Preset concentration gradient threshold (Unit: mol / m^{4}); Preset coarsening threshold (Usually below the encryption threshold).

[0044] Mesh refinement and coarsening triggering: Encryption conditions: If a certain area or If this is the case, then the grid encryption in that area will be triggered.

[0045] Encryption operation: Subdivide the grid cells into smaller cells (e.g., halve the grid size in a structured grid; perform local subdivision in an unstructured grid).

[0046] The coarsening condition is: at a preset time interval Scan the gradient of physical quantities, if and This triggers mesh coarsening. The coarsening operation merges adjacent small mesh cells into larger cells; for example, in unstructured meshes, a mesh merging algorithm is used.

[0047] The electrochemical field uses a structured grid, such as a rectangular or hexahedral grid, to facilitate the discretization of diffusion and potential equations. The mechanical force field uses an unstructured grid, such as a triangular or tetrahedral grid, to accommodate complex geometries. Interpolation methods are used to transfer physical field data in real time between different grid types.

[0048] It should be noted that the computational tasks of the lattice Boltzmann method for the mesoscale model and the multiphysics solution tasks for the macroscale model are decomposed and executed in parallel across multiple GPU cores. The mesh points of the porous network model are assigned to GPU threads, with each thread handling the distribution function update for one lattice point. The collision and migration steps of the LBM are naturally parallel, suitable for GPU implementation; the solution of the multiphysics coupled equations uses a GPU-accelerated iterative solver. Utilizing GPU parallel computing to accelerate simulation can effectively improve the efficiency of sodium-ion battery simulation.

[0049] This invention presents a multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation. It extracts the sodium-ion diffusion barrier from a microscale model and converts it into the diffusion coefficient. A mesoscale model then simulates ion transport within the electrodes to obtain key transport parameters, ensuring the microscopic correlation of macroscopic simulation input parameters. This overcomes the shortcomings of traditional macroscopic models that neglect the microstructure of materials, improving simulation accuracy and enabling simulation results to more accurately reflect the actual performance of the battery. Simultaneously, the adaptive mesh generation can respond to the distribution of macroscopic physical fields in real time. This not only avoids the waste and inefficiency caused by fixed fine meshes but also solves the problem of fixed coarse meshes failing to identify key details, reducing computational load while ensuring simulation accuracy in core areas. By combining the orderly transfer of parameters across scales with the dynamic adaptation of the adaptive mesh, the scale transition error is effectively reduced, enabling real-time response in the simulation of large-scale energy storage systems.

[0050] Specifically, in a preferred embodiment of this application, please refer to... Figure 4 The process of real-time monitoring of the physical field distribution during the simulation of the macroscopic model, and performing adaptive mesh generation based on the physical field distribution, includes: During the simulation of the macroscopic model, the temperature and concentration gradients of each region are calculated in real time. For the temperature field T and the concentration field c, calculate the magnitude of their gradients. Taking two dimensions as an example, the gradient calculation is as follows: The partial derivatives can be calculated using the central difference method, for example: If the temperature and / or sodium ion concentration gradient in each region is higher than the corresponding preset grid threshold, the grid of that region will be finer; otherwise, the grid of that region will be coarser.

[0051] Set the corresponding preset temperature gradient encryption threshold. and concentration gradient encryption threshold For each grid cell (i,j): like or If so, then the grid cell is encrypted.

[0052] like and If so, then the grid cell is coarsened.

[0053] Encryption involves dividing the current grid cell into smaller cells; coarsening involves merging the current grid cell with its neighboring cells. For example... Figure 5Comparison of adaptive grid division effects.

[0054] In this embodiment, by dynamically adjusting the computational grid, when a local temperature or sodium ion concentration gradient is detected to exceed a preset threshold, the grid in that region is automatically refined. At the same time, the grid is coarsened in regions with gentle gradients, and the released computational resources are dynamically redistributed to high-gradient regions to achieve optimized allocation of computational resources. That is, based on the temperature and concentration gradients calculated in real time during the simulation, the grid in high-gradient regions is automatically refined and the grid in low-gradient regions is coarsened, thereby prioritizing the concentration of limited computational resources in key regions where physical quantities change drastically.

[0055] Specifically, in a preferred embodiment of this application, the real-time monitoring of the physical field distribution state and the adaptive meshing based on the physical field distribution state further includes: The physical quantity gradients in the simulation process are scanned at preset time intervals, and mesh merging is performed on regions where the gradient value is lower than the preset coarsening threshold.

[0056] By setting a preset coarsening threshold Typically, the coarsening threshold is lower than the encryption threshold, i.e.: In practice, a coarsening execution cycle is set, meaning that a global coarsening scan and merging operation is triggered after each simulation time step of the coarsening cycle. The coarsening cycle can be performed only once every 50-100 simulation time steps. By executing at certain time intervals, rather than at every time step, excessively frequent mesh operations can be avoided, which would lead to excessive computation.

[0057] At the end of each time step, the simulator checks whether the current step number is an integer multiple of the coarsening period.

[0058] If not, skip all coarsening logic and proceed directly to the calculation of the next time step.

[0059] If so, a complete coarsening process is triggered, ensuring that the coarsening operation does not occur at every time step.

[0060] Once the coarsening process is triggered, the mesh is scanned. For each previously refined fine mesh cell, its current temperature gradient and concentration gradient are calculated. These two gradient values ​​are compared with a preset coarsening threshold. Only when a cell's temperature gradient is below the temperature coarsening threshold and its concentration gradient is also below the concentration coarsening threshold is the cell marked as a coarsening candidate. All candidate cells are collected into a pending list.

[0061] In the list of cells to be processed, the mesh data structure is examined to identify all sub-mesh cells (sibling cells) generated by the same parent mesh. Only when all sub-mesh cells generated by a given parent mesh are present in the coarsening candidate list are these sub-mesh cells allowed to be merged, restoring the original parent mesh. For example, for the candidate set... The cells in the array are merged. Let there be a parent cell. After being encrypted, a set of sub-units were generated. Merging is only allowed if all sub-units belong to the candidate set: In this embodiment, a unanimous merging rule prevents the accidental deletion of critical meshes in boundary regions where the physical field changes drastically. If refinement and coarsening are performed at every time step, the mesh may oscillate frequently between fine-coarse-fine-coarse states in regions where the physical field gradient is near the refinement / coarsening threshold. This oscillation introduces serious numerical errors and contaminates the simulation results. Periodic coarsening, together with the threshold hysteresis region, ensures the relative stability of the mesh topology. In addition, periodic coarsening can promptly reclaim unnecessary fine meshes, maintaining computational resources at an optimized level that matches the current physical field complexity, achieving a dynamic balance of computational load.

[0062] Specifically, in a preferred embodiment of this application, the simulation process of the macroscopic scale model further includes: Appropriate mesh types are selected based on the characteristics of different physical fields. Structured meshes are used for electrochemical fields, while unstructured meshes are used for mechanical force fields. Real-time data exchange between meshes is achieved through overlapping meshes. The structured meshes are hexahedral meshes, and the unstructured meshes are tetrahedral meshes. In practical implementation, a regular structured mesh is generated within the macroscopic computational domain of the battery, including the positive electrode, separator, and negative electrode. This mesh consists of neatly arranged hexahedral units, dividing the battery space into regular small cubes. This mesh will serve as the primary carrier for solving electrochemical governing equations such as ion concentration distribution and potential distribution. For solid structures such as electrode active material particles and current collectors, an unstructured mesh is generated. This mesh is composed of irregular tetrahedral units, capable of filling and conforming to any complex and irregular geometric shape, describing the true morphology of the electrode particles. This mesh will be used to calculate mechanical responses such as stress and strain.

[0063] Establish overlapping mesh systems and enable data exchange. The two mesh systems overlap spatially and exist simultaneously. They each have their own independent mesh cells and nodes, but together cover the entire or part of the simulation area.

[0064] From Electrochemical Field to Mechanical Force Field: The sodium ion concentration distribution calculated on a hexahedral mesh is the root cause of volume changes and stress in the electrode material. An efficient search algorithm locates the position of each tetrahedral mesh node within the hexahedral mesh. Then, shape function interpolation is used to transfer the concentration values ​​from the hexahedral mesh nodes to the tetrahedral mesh nodes as input for mechanical calculations.

[0065] From mechanical force field to electrochemical field: The stress distribution calculated on the tetrahedral mesh, in turn, affects the pore structure and ion diffusion properties of the electrode material. Similarly, stress data is transferred from the tetrahedral mesh back to the hexahedral mesh using interpolation methods to update the material parameters in the electrochemical model.

[0066] Within a simulation time step, the system solves the electrochemical equations on a hexahedral mesh to obtain new concentration and potential fields; and solves the mechanical equations on a tetrahedral mesh to obtain new stress fields. Through this data interaction, the two physical fields provide each other with the key parameters needed, thus achieving a fully coupled electrochemical-mechanical simulation. This process is repeated at each time step, dynamically simulating the charging and discharging process of the battery.

[0067] Specifically, in a preferred embodiment of this application, the preset cross-scale parameter transmission channel is a bidirectional feedback channel; Please see Figure 6 After the macroscopic model completes the multiphysics coupling simulation, the average electrode current density and temperature field distribution obtained in the macroscopic model simulation are fed back to the microscopic model to correct the boundary conditions and temperature parameters in the density functional theory calculation in the microscopic model, and to recalculate the diffusion barrier and iteratively update the diffusion coefficient.

[0068] After the initial or Nth cycle of macroscopic simulation is completed, two key feature parameters are extracted from the simulation results: the average current density of the electrodes and the temperature field distribution of the entire battery domain. The temperature field distribution of the entire battery domain includes the highest temperature, the lowest temperature, and the volume-weighted average temperature.

[0069] The characteristic parameters obtained from macroscopic simulation are fed back to the microscopic scale model to correct its calculation conditions. Temperature parameter correction: Microscale DFT calculations no longer use a fixed room temperature. In the new iterative cycle, the volume-weighted average temperature fed back from the macroscale is used as the new calculation temperature, which more realistically reflects the thermal environment of the battery during actual operation.

[0070] Boundary Conditions and Model Correction: When the feedback electrode average current density indicates that the battery is under high-rate charge / discharge, the microscale model can consider higher-order effects. For example, high current may cause changes in the local charge distribution on the electrode surface, thereby affecting the adsorption and desorption energy barriers of sodium ions. The microscale model can adjust its calculated surface model or apply an equivalent electric field to simulate these boundary condition changes at high rates.

[0071] Thermal stress effect: The non-uniform temperature field of the feedback suggests that the material may have thermal strain. Based on this, the microscale model can be used to further calculate the diffusion energy barrier under the action of the thermal strain field.

[0072] Using the corrected temperature parameters and boundary conditions, the density functional theory calculations were re-performed on the microscale model. Subsequently, the updated diffusion coefficient was calculated again using the Arrhenius formula with the new volume-weighted average temperature.

[0073] in, For the updated diffusion coefficient; For the newer diffusion barrier; The temperature is a volume-weighted average.

[0074] Traditional unidirectional data transfer is based on ideal, fixed microscopic calculation conditions, while actual batteries operate in complex environments with varying temperatures and currents. In this embodiment, the input of the microscopic calculation is corrected in real time through feedback, enabling the lowest-level material parameters to dynamically respond to macroscopic operating conditions and reducing systematic errors caused by the mismatch between model conditions and actual conditions.

[0075] Specifically, in a preferred embodiment of this application, please refer to... Figure 7 The preset grid threshold is adjusted based on the real-time charge and discharge state of the battery. During the constant current charging stage, the first set of encryption thresholds is used; during the constant voltage charging stage, the second set of encryption thresholds is used; the first set of encryption thresholds is lower than the second set of encryption thresholds.

[0076] In practice, at each time step of the macroscopic model simulation, the battery's terminal voltage and current are continuously monitored. When the charging current is maintained at a constant value and the battery voltage has not yet reached the charging cutoff voltage, it is determined to be in the constant current charging stage. When the battery voltage reaches and is clamped at this voltage, and the charging current begins to decay naturally, it is determined to have entered the constant voltage charging stage.

[0077] Two different sets of mesh refinement thresholds were preset: the first set of thresholds was used for the constant current charging stage, including a first temperature gradient threshold and a first concentration gradient threshold; the second set of thresholds was used for the constant voltage charging stage, including a second temperature gradient threshold and a second concentration gradient threshold. The first set of thresholds was lower than the second set of thresholds.

[0078] When the determination of the working stage changes, such as switching from constant current to constant voltage, the currently used encryption threshold is switched from the first group to the second group.

[0079] Using a more sensitive first set of thresholds during the constant current charging phase makes mesh refinement conditions easier to meet due to the lower threshold. Even a relatively small temperature or concentration gradient can trigger mesh refinement. During this phase, the current is constant, and ions continuously and rapidly embed into the electrode, leading to drastic changes in ion concentration within the electrode, particularly near the surface of the active material particles, resulting in large gradients. Simultaneously, electrochemical reaction heat and Joule heating are also significant. Using a low threshold ensures that mesh refinement is performed as early and densely as possible in these rapidly changing physical fields, capturing potentially sharp gradients at high resolution.

[0080] During the constant-voltage charging phase, a more lenient second set of thresholds is used, resulting in stricter mesh refinement conditions. Only regions with large gradients are refined. Upon entering the constant-voltage phase, the current gradually decreases, the ion embedding rate slows, and the internal chemical reactions and mass transfer processes become more gradual. The overall physical field distribution of the system becomes relatively smooth, no longer producing drastic transients. At this point, using a higher threshold means the system will tolerate more low-to-medium gradient regions, allowing the mesh in these regions to remain or degenerate into a coarser state, thus saving computational resources.

[0081] Throughout the simulation, a continuous cycle of identification and switching ensures that the mesh adaptive strategy always matches the real-time dynamic characteristics of the battery. During the constant-current phase, where the physical field changes drastically, a low threshold ensures that computational resources are concentrated in the most critical areas, preventing the loss of important physical details due to insufficient mesh density. During the constant-voltage phase, where the physical field changes gradually, a high threshold reduces the number of unnecessary fine meshes, thereby lowering the computational load and memory usage in subsequent time steps. This on-demand allocation strategy maximizes overall computational efficiency compared to using a single fixed threshold throughout the simulation.

[0082] Those skilled in the art will recognize that the units of the various examples described in connection with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of the invention.

[0083] In the embodiments provided by the present invention, it should be understood that the division of units is only a logical functional division. In actual implementation, there may be other division methods, such as multiple units can be combined into one unit, one unit can be split into multiple units, or some features can be ignored.

[0084] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0085] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the specification of the present invention.

Claims

1. A multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation, characterized in that, include: Establish a multi-scale simulation model for sodium-ion batteries, including microscale, mesoscale, and macroscale models; Based on the preset cross-scale parameter transfer channel, the diffusion coefficient output by the microscale model is transferred to the mesoscale model. The transfer parameters are obtained by simulating ion transport within the electrode. The transfer parameters are then transferred to the macroscale model to perform multi-physics coupling simulation of sodium-ion batteries. In the process of multi-physics coupling simulation of sodium-ion batteries in the macro-scale model, the physical field distribution is monitored in real time, and adaptive mesh generation is performed based on the physical field distribution.

2. The multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation according to claim 1, characterized in that, The establishment of a multi-scale simulation model for sodium-ion batteries, including microscale, mesoscale, and macroscale models, includes: The microscale model was constructed, and the diffusion barrier of sodium ions in hard carbon anode material was calculated using density functional theory. The diffusion barrier was then converted into the diffusion coefficient. The mesoscale model is constructed based on the pore network model of the electrode microstructure, and the lattice Boltzmann method is used to simulate the transport process of electrolyte and sodium ions in the pore network model, and the transport parameters are obtained, wherein the diffusion coefficient output by the microscale model is used as the input parameter. The macroscopic-scale model is constructed by establishing a multiphysics coupling model that integrates electrochemical field, temperature field and structural stress field based on multiphysics coupling simulation. This model is used to simulate the external characteristics and internal state of the battery during charging and discharging. The output parameters of the mesoscopic-scale model are imported into the multiphysics coupling model.

3. The multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation according to claim 1, characterized in that, The process of real-time monitoring of the physical field distribution during the simulation of the macroscopic model, and the execution of adaptive mesh generation based on the physical field distribution, includes: During the simulation of the macroscopic model, the temperature and concentration gradients of each region are calculated in real time. If the temperature and / or sodium ion concentration gradient in each region is higher than the corresponding preset grid threshold, the grid of that region will be finer; otherwise, the grid of that region will be coarser.

4. The multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation according to claim 3, characterized in that, The real-time monitoring of the physical field distribution state and the execution of adaptive mesh generation based on the physical field distribution state further include: The physical quantity gradients in the simulation process are scanned at preset time intervals, and mesh merging is performed on regions where the gradient value is lower than the preset coarsening threshold.

5. The multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation according to claim 3, characterized in that, The simulation process of the macroscopic model also includes: To suit different physical field characteristics, a suitable mesh type is selected. The electrochemical field uses a structured mesh, while the mechanical force field uses an unstructured mesh. Real-time data interaction between meshes is achieved through overlapping meshes.

6. The multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation according to claim 2, characterized in that, The conversion formula for the diffusion barrier to the diffusion coefficient is as follows: Among them, E a D is the diffusion barrier; D is the diffusion coefficient; is the pre-exponential factor; R is the universal gas constant; T is the absolute temperature.

7. The multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation according to any one of claims 3, characterized in that, The preset cross-scale parameter transmission channel is a bidirectional feedback channel; After the macroscopic model completes the multiphysics coupling simulation, the average electrode current density and temperature field distribution obtained from the macroscopic model simulation are fed back to the microscopic model to correct the boundary conditions and temperature parameters in the density functional theory calculation in the microscopic model, and to recalculate the diffusion barrier and iteratively update the diffusion coefficient.

8. The multi-scale simulation method for sodium-ion batteries based on adaptive mesh generation according to claim 3, characterized in that, The preset grid threshold is adjusted based on the real-time charge and discharge status of the battery: During the constant current charging stage, the first set of encryption thresholds is used; during the constant voltage charging stage, the second set of encryption thresholds is used; the first set of encryption thresholds is lower than the second set of encryption thresholds.

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