A fluid-structure interaction numerical simulation method and system based on a voxel grid
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NINGXIA UNIVERSITY
- Filing Date
- 2026-03-10
- Publication Date
- 2026-06-12
AI Technical Summary
Existing technologies for numerical simulation of fluid-structure interaction suffer from problems such as low accuracy in the modeling of complex geometries, huge memory consumption of large-scale stiffness matrices, and difficulty in efficient implementation on GPUs.
The STL model is converted into a voxel mesh using a high-precision stochastic Monte Carlo voxelization method, and the fluid field is calculated using the lattice Boltzmann method. The solid mechanics problem is solved by combining the matrix-free conjugate gradient method, and the matrix-free stiffness matrix is calculated using a spring network model.
It achieves high-precision fluid-structure interaction simulation, reduces memory consumption, improves GPU parallel computing efficiency, is applicable to fluid-structure interaction problems with complex topologies and dynamic boundaries, and expands the scope of engineering applications.
Smart Images
Figure CN122197709A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the interdisciplinary field of computational fluid dynamics and solid mechanics, and in particular to a method and system for numerical simulation of fluid-structure interaction based on voxel meshes. Background Technology
[0002] Fluid-structure interaction (FSI) is one of the core challenges in computational mechanics, and it is widely present in many important fields such as aerospace (e.g., wing flutter), biomedicine (e.g., blood flow and blood vessel wall interaction), and civil engineering (e.g., building response under wind load). Efficient and accurate numerical simulation of these problems is crucial for engineering design and safety assessment.
[0003] Traditional numerical methods for fluid-structure interaction typically employ separate fluid and solid domain meshes. The core challenge of these methods lies in the need for complex mesh mapping and data interpolation at dynamically changing fluid-structure interfaces. This not only leads to high computational costs and complex algorithm implementations, but also presents serious challenges when dealing with geometries with complex topologies, thin walls, or large deformation characteristics, such as mesh distortion, reconstruction difficulties, and even computational failure.
[0004] In recent years, methods combining the Lattice Boltzmann Method (LBM) with submerged boundary / voxelation have offered new approaches to handling complex flow boundaries. LBM, with its inherent parallelism and good adaptability to complex boundaries, has shown significant advantages in fluid simulations; while unified voxel meshes promise to circumvent the cumbersome interface processing of traditional methods. However, existing solutions still have significant limitations: in solid mechanics solutions, most research still relies on the traditional finite element method, requiring explicit assembly and storage of large-scale global stiffness matrices. This makes the memory consumption for high-resolution 3D problems extremely high, making it difficult to run efficiently on parallel computing devices such as consumer-grade graphics processing units (GPUs), thus limiting its application in practical engineering problems. On the other hand, in the preprocessing stage of converting computer-aided design (CAD) models (such as STL triangular facets) into voxel meshes, the commonly used methods based on fixed offset ray projection or single-precision calculation are prone to producing incorrect "penetration" or "missed judgment" due to numerical errors when dealing with geometry with thin-walled structures, sharp diagonals or high curvature features, resulting in geometric distortion, which in turn seriously affects the accuracy and numerical stability of subsequent fluid-structure interaction simulations.
[0005] Therefore, existing technologies urgently need a fluid-structure interaction numerical simulation solution that can simultaneously meet the following requirements: First, a high-precision and robust geometric voxelization preprocessing method that can reliably transform complex models without introducing geometric defects; Second, the development of a fluid-structure interaction solution framework based entirely on a unified voxel mesh that does not require explicit assembly of stiffness matrices, thereby achieving memory-efficient and GPU-accelerated high-performance computing to meet the needs of large-scale 3D engineering simulation. Summary of the Invention
[0006] The purpose of this invention is to provide a method and system for numerical simulation of fluid-structure interaction based on voxel meshes, in order to solve the problems of low fidelity of complex geometric voxelization, huge memory consumption of large-scale stiffness matrices, and difficulty in efficiently implementing full-process fluid-structure interaction simulation on GPUs.
[0007] To achieve the above objectives, this invention provides a numerical simulation method for fluid-structure interaction based on voxel meshes, comprising the following steps: Step S1: Convert the input STL triangular facet model into a voxel mesh using a voxelization method, and generate a solid node mask based on the solid voxel marker field. Step S2: Based on the obtained voxel grid, the velocity field, pressure field and density field of the fluid are calculated in the fluid voxel region using the lattice Boltzmann method; Step S3: Based on the calculated pressure field, the fluid pressure is converted into external force on the solid node by applying a direct interface load, thereby obtaining the node external force field; Step S4: Based on the obtained nodal external force field, the linear elastic statics problem is solved using the matrix-free conjugate gradient method to obtain the displacement field of the solid nodes; Step S5: Output the displacement field of the solid node obtained in step S4, the external force field of the node obtained in step S3, and the solid node mask generated in step S1 for visualization.
[0008] Preferably, the voxelization method in step S1 is a high-precision randomized Monte Carlo voxelization method, specifically including: Vertex coordinates and face indices are stored using double-precision floating-point numbers; The ray projection performs multiple rounds of independent random voxel offsets, and in each round, the offset is uniformly and randomly selected within the voxel, and the ray is emitted along a fixed direction; Calculate the depth of the intersection point between the ray and the triangle face, collect and sort the intersection depths; For each voxel center, apply the parity rule to determine whether the sample is solid, and accumulate the vote count; The final solid / fluid properties are determined based on a preset voting threshold, and a solid voxel labeling field is generated.
[0009] Preferably, the number of rounds of light projection for multiple rounds of independent random sub-voxel offset is 20 to 50; the random offset is uniformly selected within a range of ±0.4 times the voxel size; the fixed direction is the Z-axis direction; and the preset voting threshold is 0.2 to 0.5 times the total number of samples.
[0010] Preferably, in step S1, the generated solid node mask includes: defining the condition for a node to be a solid node as at least one of its eight adjacent voxels being a solid voxel, based on the solid voxel labeling field, thereby generating a solid node mask.
[0011] Preferably, in step S2, the lattice Boltzmann method uses the D3Q19 model, and the pressure field is calculated using the ideal gas equation of state.
[0012] Preferably, in step S3, the direct interface load application method specifically includes: Traverse the six adjacent faces of each solid voxel. If the adjacent voxel is a fluid, calculate the fluid pressure force at the interface and apply the force uniformly to the four nodes of the face to obtain the nodal external force field.
[0013] Preferably, in step S4, the matrix-vector product of the stiffness matrix is calculated in a matrix-free manner using the spring network model. Specifically, this includes: in each conjugate gradient iteration, for each solid voxel, its 12 internal edges are treated as linear springs, the difference between the current search direction vectors at the two endpoints is calculated, multiplied by the spring stiffness coefficient to obtain the spring force contribution, and the spring force contribution is accumulated to the corresponding node to form the product of the stiffness matrix and the current search direction vector; and during the iteration process, boundary condition constraints are uniformly applied to the displacement, residual, search direction, and stiffness matrix-vector product until convergence is obtained to obtain the nodal displacement field.
[0014] Preferably, the stiffness coefficient of the linear spring on each edge in the spring network model is set based on the Young's modulus of the solid material; the convergence criterion for the conjugate gradient iteration is that the relative residual is less than a preset threshold.
[0015] Preferably, in step S4, the boundary conditions include free boundaries, fixed boundaries, and symmetrical boundaries.
[0016] This invention also provides a voxel-grid-based fluid-structure interaction numerical simulation system for implementing the voxel-grid-based fluid-structure interaction numerical simulation method described above, comprising: The voxelization module is used to convert the input STL triangular facet model into a voxel mesh using a voxelization method, and generate a solid node mask based on the solid voxel marker field. The fluid solver module is used to calculate the velocity, pressure and density fields of the fluid in the fluid voxel region based on the obtained voxel mesh and using the lattice Boltzmann method. The load conversion module is used to convert fluid pressure into external forces on solid nodes based on the calculated pressure field by applying direct interface loads, thereby obtaining the nodal external force field. The solid solution module is used to solve linear elastic-static problems based on the obtained nodal external force fields using the matrix-free conjugate gradient method, and obtain the displacement fields of solid nodes; wherein, the matrix-vector product of the stiffness matrix is calculated in a matrix-free manner through the spring network model; The boundary constraint module is used to uniformly apply boundary condition constraints to the displacement, residual, search direction, and stiffness matrix-vector product results during the solution process of the matrix-free conjugate gradient method. The output module is used to output the nodal displacement field, nodal external force field, and solid nodal mask for visualization.
[0017] Therefore, the present invention employs the above-mentioned method and system for numerical simulation of fluid-structure interaction based on voxel meshes, and the beneficial technical effects are as follows: (1) To address the problem that existing voxelization methods are prone to numerical penetration and missed detection in thin-walled, diagonal, and high-curvature regions when converting complex STL models, this invention adopts a high-precision Monte Carlo voxelization method based on double-precision calculation, multi-round random sub-voxel offset ray projection, and voting mechanism. This method effectively eliminates the inherent "diagonal blind zone" and thin-wall penetration defects of traditional fixed offset methods through statistical significance determination, and can reliably convert arbitrarily complex triangular facet models into high-fidelity unified voxel meshes, laying an accurate geometric foundation for subsequent high-precision fluid-structure interaction simulations.
[0018] (2) To address the problem that traditional methods suffer from huge memory consumption and difficulty in running on consumer-grade GPUs due to the explicit assembly and storage of large-scale finite element stiffness matrices, the core innovation of this invention lies in using a "spring network" model to mechanically discretize solid voxels, and based on this, implementing a matrix-free conjugate gradient solver. During the iteration process, this solver implicitly performs the product operation of the stiffness matrix and vector by traversing the springs within the voxels and accumulating local force contributions, completely avoiding the storage and manipulation of explicit stiffness matrices. This fundamental change enables high-resolution three-dimensional solid mechanics problems to be solved efficiently with the limited memory resources of GPUs, achieving a fully parallel GPU acceleration from fluid dynamics (LBM) computation to solid solution.
[0019] (3) This invention integrates fluid simulation, fluid-structure interaction load transfer (direct interface mapping), and solid mechanics solution (matrix-free CG) onto a unified voxel mesh, eliminating the complex interface mesh mapping and data interpolation steps required by traditional separate meshing methods. This integrated design not only simplifies algorithm implementation and reduces accuracy loss and computational overhead caused by data conversion, but also achieves significant end-to-end performance improvement because each step is highly adapted to the GPU parallel architecture. This method is particularly suitable for fluid-structure interaction problems with complex topologies or dynamic boundaries, significantly improving simulation efficiency while ensuring computational accuracy, and expanding the application scope of high-performance fluid-structure interaction simulation in engineering practice. Attached Figure Description
[0020] Figure 1 This is a flowchart of the fluid-structure interaction numerical simulation method based on voxel meshes according to the present invention; Figure 2 This is a schematic diagram of a model in an embodiment of the present invention, wherein... Figure 2 A is the geometric model diagram. Figure 2 B is the corresponding generated STL triangle patch model diagram; Figure 3 This is a schematic diagram of the overall mesh of the voxelized model in an embodiment of the present invention; Figure 4 This is a schematic diagram of the voxelized mesh in an embodiment of the present invention, wherein... Figure 4 In the diagram, A represents the solid region mesh. Figure 4 In the diagram, B represents the fluid region mesh. Figure 5 This is a diagram showing the results of simulating the fluid region using the D3Q19 model in an embodiment of the present invention. Figure 5 In the diagram, A represents the velocity field contour plot. Figure 5 B in the diagram represents the pressure field contour plot; Figure 6 This is a schematic diagram of the velocity field of the flow field section in an embodiment of the present invention, wherein... Figure 6 In the diagram, A represents the velocity field contour plot of the cross-section of the protruding part of the structure. Figure 6 B in the diagram represents the velocity field contour plot of the concave section of the structure. Figure 7 This is a schematic diagram of the pressure field at a cross-section of the flow field in an embodiment of the present invention, wherein... Figure 7 In the diagram, A represents the pressure field contour plot of the cross-section of the protruding part of the structure. Figure 7 B in the diagram represents the pressure field contour plot of the concave section of the structure. Figure 8 This is a schematic diagram of the velocity vector of the flow field cross section in an embodiment of the present invention, wherein... Figure 8 In the diagram, A represents the velocity vector diagram of the cross-section of the protruding part of the structure. Figure 8In the diagram, B represents the velocity vector diagram of the cross-section of the concave part of the structure. Figure 9 This is a schematic diagram of the interface load where fluid pressure directly applies solid node force in an embodiment of the present invention; Figure 10 This is a schematic diagram of the calculation results after applying a load in an embodiment of the present invention, wherein... Figure 10 In the diagram, A represents the force contour plot of the solid surface. Figure 10 B in the diagram represents the displacement field contour plot; Figure 11 This is a schematic diagram showing a displacement magnified 400 times in an embodiment of the present invention, wherein... Figure 11 In the diagram, A represents a deformed image without grid lines. Figure 11 B in the diagram represents a deformed image with grid lines. Detailed Implementation
[0021] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.
[0022] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.
[0023] Example 1 This embodiment provides a voxel mesh-based numerical simulation method for fluid-structure interaction. This method addresses the deformation problem of three-dimensional elastic structures with complex geometries under fluid action, achieving high-performance simulation across the entire process on a consumer-grade GPU (GeForce RTX 4080 SUPER). The specific process of the method is as follows: Figure 1 As shown, it includes the following steps: (1) High-precision voxelization and node mask generation for complex geometry.
[0024] First, a three-dimensional geometric model is created according to the simulation requirements, and then converted into an STL triangle patch format as input, such as... Figure 2 As shown. This invention employs a high-precision random Monte Carlo voxelization method to discretize the STL model into a regular three-dimensional voxel mesh.
[0025] The specific implementation process is as follows: In GPU memory, double-precision floating-point numbers (float64) are used to store the vertex coordinates and face indices of the STL model to ensure numerical stability.
[0026] Perform 20-50 independent rounds of random sampling. In each round of sampling, select an offset point (within ±0.4 times the voxel side length) uniformly and randomly within each voxel, and emit a ray along a fixed direction (preferably the Z-axis).
[0027] The Moller-Trumbore algorithm was used to calculate the intersection points of each ray with all triangular facets, and the depth of the intersection points was recorded.
[0028] For each voxel center point, apply the Ray Casting Parity Count to determine whether it belongs to "solid" or "fluid" in the current sampling based on its relative position to the model surface, and accumulate the "solid" votes.
[0029] After all rounds of sampling are completed, a final determination is made based on a preset voting threshold (preferably 20%-50% of the total number of samples; this value is selected through numerical experiment calibration, which can effectively improve the accuracy of thin-walled structure detection and avoid missed or over-judgment; in this embodiment, it is set to 20% of the total number of samples, i.e., 0.2): If the cumulative number of "solid" votes for a voxel exceeds the threshold, it is marked as a solid voxel (voxel labeling field). ,in (These represent the grid indices of the voxels in the X, Y, and Z directions, respectively), otherwise they are marked as fluid voxels. This process generates a voxel-labeled field that defines the entire computational domain.
[0030] In this embodiment, the generated computational domain voxel grid resolution is voxel side length , , , This indicates the number of voxels in the X, Y, and Z directions of the voxel mesh. The overall voxelized mesh is shown below. Figure 3 As shown, the solid and fluid regions are separated and displayed as follows: Figure 4 As shown.
[0031] Subsequently, based on this voxel-labeled field, a node mask for solid mechanics calculations is generated. The node mesh size is defined as follows. A node Marked as a solid node mask, i.e., a solid node mask A node is identified if and only if at least one of its eight neighboring voxels is a solid voxel. This mask ensures that all nodes associated with solids are identified, laying the foundation for the subsequent construction of the spring network model.
[0032] (2) Fluid dynamics simulation based on the Lattice Boltzmann method (LBM).
[0033] Using the voxel grid generated in step (1), the present invention solves the motion of incompressible fluids in voxel regions marked as fluids using the Lattice Boltzmann Method (LBM).
[0034] The model and evolution adopt the D3Q19 discrete velocity model. Distribution function The evolution follows the collision-migration equation: ; in, Indicates the first The distribution function of discrete velocity directions represents the position. ,time At that time, along the first The probability distribution of particles in each direction. It is a discrete velocity vector. For relaxation time, For time step.
[0035] equilibrium distribution function It is given by the following formula: ; in, For the first Weight coefficients for each direction, For the speed of sound in a grid.
[0036] Macroscopic fluid density field and fluid velocity vector field Obtained through moment statistics of the distribution function: ; ; Pressure field calculation, fluid pressure field The calculation is performed using the ideal gas law, and this calculation directly depends on the density field obtained above. : ; in, For reference density, It is the square of the speed of sound.
[0037] Therefore, this step explicitly calculates and obtains three key fluid fields: the velocity field... Density field and pressure field Among them, the pressure field It is the direct input for subsequent fluid-structure interaction load transfer, while the density field It is an essential intermediate variable for calculating the pressure field.
[0038] In this embodiment, the inlet is set to a uniform inflow in the X direction with a velocity of 0.1 grid units. After sufficient iterations, the flow field reaches a quasi-steady state, and the calculated steady-state velocity and pressure fields are as follows. Figure 5 As shown. The velocity contour map, pressure contour map, and velocity vector distribution of a specific cross-section are respectively as follows: Figure 6 , Figure 7 and Figure 8 As shown.
[0039] (3) Direct mapping of fluid-structure interaction interface loads.
[0040] The global pressure field calculated in step (2) As input, this invention applies fluid pressure loads to a solid structure through a direct mapping mechanism, thereby obtaining the nodal external force fields that drive the deformation of the solid. .
[0041] The specific process is as follows: traverse each voxel marked as solid. Examine its six adjacent faces. If an adjacent voxel is fluid, calculate the force exerted by the fluid pressure on that interface and distribute this force evenly to the four solid nodes constituting that face. Take the left face (normal direction is...) as an example. For example, if adjacent voxels If it is a fluid, then the resultant pressure force on the interface is... for: ; The resultant force is evenly distributed across the nodes. , , , Each node receives one-quarter of the force contribution. After performing the above operation on all six faces of all solid voxels, all contributions are accumulated to the corresponding solid nodes to obtain the complete nodal external force field. The process is illustrated in the diagram below. Figure 9 As shown.
[0042] (4) Solid mechanics solution based on spring network and matrix-free conjugate gradient method (including boundary condition treatment).
[0043] The nodal external force field calculated in step (3) Using the load input and the solid node mask and voxel connection relationship defined in step (1) as the geometric and topological basis, this invention employs a matrix-free conjugate gradient method to solve linear elastic statics problems in order to obtain the displacement field of the solid structure. .
[0044] Physical model: The solid material satisfies a linear elastic constitutive relation, and the equilibrium equation is: ; ; in, For divergence operators, Let Cauchy be the stress tensor. For unit tensors, For small strain tensors, It is the transpose symbol. and Let be Lamé's constant.
[0045] Calculation of stiffness without matrix: This invention does not explicitly assemble the total stiffness matrix. Instead, utilizing the regularity of the voxel mesh in step (1), the 12 edges (connecting its 8 corner nodes) inside each solid voxel are modeled as linear springs, and the spring stiffness coefficient is... Based on Young's modulus of solid materials voxel side length Set as .
[0046] In the conjugate gradient iteration, the stiffness matrix is calculated. with vector product At that time, it is only necessary to traverse all the springs within the solid voxels: for the connection nodes and For a spring, calculate the difference between the search direction vectors at its two endpoints. Multiplied by the spring stiffness coefficient Obtain the spring force contribution vector: ; Then Forward accumulation to node Accumulate in reverse to the node (Saving the balance between action and reaction forces), that is: ; ; in, Represents a node The stiffness motion vector at that point, Indicates the node after accumulation The stiffness motion vector at that point, Represents a node The stiffness motion vector at that point, Indicates the node after accumulation The stiffness motion vector at that point.
[0047] This operation implicitly simulates the mechanical effects of the stiffness matrix through a local spring network, completely avoiding the storage and manipulation of large-scale explicit stiffness matrices, making it particularly suitable for parallel implementation on GPUs.
[0048] Iterative solution process: Initialization: Set initial values for the displacement field Initial residual vector Initial search direction vector And immediately apply boundary conditions.
[0049] Iterative solution: For Repeat the following steps until convergence: ; ; ; ; ; in, The number of iterations. For the first The step size factor, For the first The residual vector during each iteration. For the first The search direction vector during each iteration. For the first The displacement vector field during each iteration. for The conjugate coefficient of the step.
[0050] Boundary condition handling: in each update , , , Subsequently, a unified boundary condition handling function is invoked to ensure that the solution satisfies the constraints. This invention supports three types of boundaries: fixed boundary, free boundary, and symmetric boundary. In each conjugate gradient iteration, all relevant vector fields (residual vectors) are processed through a unified constraint function. Search direction vector Displacement field Stiffness motion vector For fixed boundary nodes, all their displacement / force components are set to zero; for symmetrical boundary nodes, the displacement components in the normal direction of the boundary surface are set to zero.
[0051] Convergence Criterion: In this embodiment, the convergence criterion is set as relative residual. .
[0052] In this embodiment, the bottom of the solid structure is set as a fixed boundary ( The top is a free boundary, and the surrounding area is a symmetrical boundary (normal displacement is zero). After the solution is completed, the pressure distribution and final displacement field on the solid surface are as follows: Figure 10 As shown.
[0053] (5) Results output and visualization.
[0054] Finally, the calculation results of the aforementioned core steps are collected and output: the nodal displacement field obtained in step (4), the nodal external force field obtained in step (3), and the solid nodal mask generated in step (1) are exported together as a VTK format file. This format file can be directly read by standard scientific visualization software such as ParaView and used to generate various cloud maps, vector maps, and deformation animations. In this embodiment, the deformation results of the solid domain under fluid load (displacement magnified 400 times for clear display) are as follows: Figure 11 As shown.
[0055] Example 2 A fluid-structure interaction numerical simulation system based on voxel meshes includes: The voxelization module is used to convert the input STL triangular facet model into a voxel mesh using a voxelization method, and generate a solid node mask based on the solid voxel marker field. The fluid solver module is used to calculate the velocity, pressure and density fields of the fluid in the fluid voxel region based on the obtained voxel mesh and using the lattice Boltzmann method. The load conversion module is used to convert fluid pressure into external forces on solid nodes based on the calculated pressure field by applying direct interface loads, thereby obtaining the nodal external force field. The solid solution module is used to solve linear elastic-static problems based on the obtained nodal external force fields using the matrix-free conjugate gradient method, and obtain the displacement fields of solid nodes; wherein, the matrix-vector product of the stiffness matrix is calculated in a matrix-free manner through the spring network model; The boundary constraint module is used to uniformly apply boundary condition constraints to the displacement, residual, search direction, and stiffness matrix-vector product results during the solution process of the matrix-free conjugate gradient method. The output module is used to output the nodal displacement field, nodal external force field, and solid nodal mask for visualization.
[0056] It is worth noting that all contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.
[0057] Therefore, the present invention adopts the above-mentioned method and system for fluid-structure interaction numerical simulation based on voxel mesh, which effectively solves the problems of low geometric voxelization accuracy, large memory consumption and difficulty in efficient implementation on GPU in traditional fluid-structure interaction simulation. It realizes an integrated simulation scheme from complex geometric processing to high-performance solution of the whole process, which significantly improves computational efficiency and engineering applicability.
[0058] 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.
Claims
1. A numerical simulation method for fluid-structure interaction based on voxel meshes, characterized in that, Includes the following steps: Step S1: Convert the input STL triangular facet model into a voxel mesh using a voxelization method, and generate a solid node mask based on the solid voxel marker field. Step S2: Based on the obtained voxel grid, the velocity field, pressure field and density field of the fluid are calculated in the fluid voxel region using the lattice Boltzmann method; Step S3: Based on the calculated pressure field, the fluid pressure is converted into external force on the solid node by applying a direct interface load, thereby obtaining the node external force field; Step S4: Based on the obtained nodal external force field, the linear elastic statics problem is solved using the matrix-free conjugate gradient method to obtain the displacement field of the solid nodes; Step S5: Output the displacement field of the solid node obtained in step S4, the external force field of the node obtained in step S3, and the solid node mask generated in step S1 for visualization.
2. The method for numerical simulation of fluid-structure interaction based on voxel meshes according to claim 1, characterized in that, The voxelization method in step S1 is a high-precision randomized Monte Carlo voxelization method, specifically including: Vertex coordinates and face indices are stored using double-precision floating-point numbers; The ray projection performs multiple rounds of independent random voxel offsets, and in each round, the offset is uniformly and randomly selected within the voxel, and the ray is emitted along a fixed direction; Calculate the depth of the intersection point between the ray and the triangle face, collect and sort the intersection depths; For each voxel center, apply the parity rule to determine whether the sample is solid, and accumulate the vote count; The final solid / fluid properties are determined based on a preset voting threshold, and a solid voxel labeling field is generated.
3. The method for numerical simulation of fluid-structure interaction based on voxel meshes according to claim 2, characterized in that, The number of rounds of ray projection for multi-round independent random sub-voxel offset is 20 to 50; the random offset is uniformly selected within the range of ±0.4 times the voxel size; the fixed direction is the Z-axis direction; and the preset voting threshold is 0.2 to 0.5 times the total number of samples.
4. The method for numerical simulation of fluid-structure interaction based on voxel meshes according to claim 1, characterized in that, In step S1, the generated solid node mask includes: based on the solid voxel labeling field, defining the condition for a node to be a solid node as at least one of its 8 adjacent voxels being a solid voxel, thereby generating a solid node mask.
5. The method for numerical simulation of fluid-structure interaction based on voxel meshes according to claim 1, characterized in that, In step S2, the lattice Boltzmann method uses the D3Q19 model, and the pressure field is calculated using the ideal gas equation of state.
6. The method for numerical simulation of fluid-structure interaction based on voxel meshes according to claim 1, characterized in that, In step S3, the direct interface load application method specifically includes: Traverse the six adjacent faces of each solid voxel. If the adjacent voxel is a fluid, calculate the fluid pressure force at the interface and apply the force uniformly to the four nodes of the face to obtain the nodal external force field.
7. The method for numerical simulation of fluid-structure interaction based on voxel meshes according to claim 1, characterized in that, In step S4, the matrix-vector product of the stiffness matrix is calculated in a matrix-free manner using the spring network model. Specifically, in each conjugate gradient iteration, for each solid voxel, its 12 internal edges are treated as linear springs. The difference between the current search direction vectors at the two endpoints is calculated, multiplied by the spring stiffness coefficient to obtain the spring force contribution, and this spring force contribution is accumulated to the corresponding node to form the product of the stiffness matrix and the current search direction vector. Boundary condition constraints are uniformly applied to the displacement, residual, search direction, and stiffness matrix-vector product during the iteration process until convergence is obtained to obtain the nodal displacement field.
8. The method for numerical simulation of fluid-structure interaction based on voxel meshes according to claim 7, characterized in that, The stiffness coefficient of the linear spring on each edge in the spring network model is set based on the Young's modulus of the solid material; the convergence criterion for the conjugate gradient iteration is that the relative residual is less than a preset threshold.
9. The method for numerical simulation of fluid-structure interaction based on voxel meshes according to claim 1, characterized in that, In step S4, the boundary conditions include free boundaries, fixed boundaries, and symmetric boundaries.
10. A fluid-structure interaction numerical simulation system based on voxel meshes, characterized in that, A method for implementing a voxel-grid-based fluid-structure interaction numerical simulation as described in any one of claims 1-9 includes: The voxelization module is used to convert the input STL triangular facet model into a voxel mesh using a voxelization method, and generate a solid node mask based on the solid voxel marker field. The fluid solver module is used to calculate the velocity, pressure and density fields of the fluid in the fluid voxel region based on the obtained voxel mesh and using the lattice Boltzmann method. The load conversion module is used to convert fluid pressure into external forces on solid nodes based on the calculated pressure field by applying direct interface loads, thereby obtaining the nodal external force field. The solid solution module is used to solve linear elastic-static problems based on the obtained nodal external force fields using the matrix-free conjugate gradient method, and obtain the displacement fields of solid nodes; wherein, the matrix-vector product of the stiffness matrix is calculated in a matrix-free manner through the spring network model; The boundary constraint module is used to uniformly apply boundary condition constraints to the displacement, residual, search direction, and stiffness matrix-vector product results during the solution process of the matrix-free conjugate gradient method. The output module is used to output the nodal displacement field, nodal external force field, and solid nodal mask for visualization.