Solid-liquid coupling simulation method based on decomposition compatibility affine particle mesh algorithm

Abstract

The invention discloses a solid-liquid coupling simulation method based on a decomposition compatible affine particle mesh algorithm, which is suitable for interaction simulation of an elastic solid and an incompressible fluid under a free slip boundary condition. The method comprises the following steps: a) describing a relationship between a grid node and a particle at a fluid-solid interface by adopting particle and grid compatibility, and providing guidance for subsequent particle-grid-particle transfer; b) using a phase field gradient method to track the fluid-solid compatibility and normal at the interface; and c) transmitting the tangential component of the speed among the incompatible grid nodes to prevent the speed among different phase fields from being smoothed, and transmitting the normal component of the speed without limitation to realize the smooth separation of the fluid-solid interface. According to the method, the non-physical viscosity in the traditional MPM method is effectively reduced, and a more accurate solid-liquid coupling simulation effect is provided.

Description

Technical Field

[0001] The present invention belongs to the field of computer graphics, and specifically is a solid-liquid coupling simulation method based on a decomposed compatibility affine particle mesh algorithm, which includes compatibility calculation based on phase field gradient, a decomposed compatibility affine particle mesh transmission algorithm, etc. Background Art

[0002] In recent decades, simulation of fluid flow and solid deformation has been crucial in the visual effects industry. In computer graphics, complex governing equations are usually discretized onto particles or meshes. Specifically, there are generally particle methods, mesh methods, and particle-mesh hybrid methods. Mesh-based methods have better stability and convenience in gradient calculation, but they will have significant numerical dissipation and have difficulties in accurately tracking geometric boundaries; particle methods are more suitable for representing large-scale deformation of objects, but are affected by numerical stability; particle-mesh hybrid methods combine the advantages of particles and meshes, which can better topological tracking and numerical stability. Material point method (MPM) is a kind of particle-mesh hybrid method, which is a generalized framework extended from particle-mesh method (PIC) and fluid implicit particle method (FLIP) to solid mechanics. MPM uses B-spline kernel function to facilitate the transfer of physical properties between particles and meshes. Particles are responsible for carrying important physical quantities such as mass, velocity, position and deformation gradient, while meshes are used to perform gradient calculations and manage collision handling. This division of tasks enables MPM to take advantage of the advantages of particles and meshes, thereby achieving more accurate and stable simulations. The affine particle-grid method (APIC) transfer scheme is usually used to exchange information between particles and grids in MPM. Although APIC does make particles more active in most cases, it still faces serious numerical viscosity problems, making it difficult to separate fluids and solids. Summary of the invention

[0003] The purpose of the present invention is to reduce the numerical viscosity of traditional MPM and obtain enhanced fluid simulation effect. A solid-liquid coupling simulation method based on decomposition compatible affine particle mesh algorithm is proposed. This method reduces the numerical viscosity of the hybrid particle mesh method with a small performance loss, and obtains a fluid-solid coupling animation effect with strong sense of reality and in line with physical laws.

[0004] The specific technical solution for achieving the purpose of the present invention is:

[0005] A solid-liquid coupling simulation method based on a decomposition compatible affine particle mesh algorithm, the method comprising the following steps:

[0006] a) Fluid-solid boundary information collection based on particle grid transmission

[0007] i) Using mass gradients to estimate particle and grid normals

[0008] First, the mass of the solid grid and the normal of the solid particle are calculated by transferring the particle to the grid:

[0009]

[0010] The superscript s indicates solid, m p is the particle mass, m i is the grid mass, w ip is the B-spline interpolation weight of grid point i and particle p, n p is the particle's normal, is the gradient operator;

[0011] Then calculate the grid point normal and fluid particle normal

[0012]

[0013] where n i is the grid point normal, is the fluid particle normal

[0014] ii) Computing the compatibility of grid points and particles

[0015] First, estimate the particle phase field gradient and the material-weighted particle phase field gradient Q p :

[0016]

[0017] where s p represents the fluid-solid phase field of the particle, s i represents the fluid-solid phase field of the grid point, both of which are 1 for fluid and 0 for solid;

[0018] Then the exact grid flow solid phase field value s is calculated i :

[0019]

[0020] Finally, the compatibility c between the grid point i and the particle p is calculated ip , if and only if s i =s p When c ip is 1.

[0021] b) Use the decomposition-compatible affine particle-mesh transfer algorithm to transfer information between particles and meshes

[0022] i) Particle-to-Grid Information Transfer (P2G)

[0023] The particle information is transferred to the grid points in the following way to ensure energy conservation:

[0024]

[0025] v i =(m i v i ) norm / m i +(m i v i ) tan / m i+

[0026] where p i+ represents the particle with the same compatibility as grid point i, p i- represents particles with different compatibility with grid point i; i p+ represents the grid point with the same compatibility as particle p, i p- represents a grid point with different compatibility with particle p, B q is the affine state matrix, D q is the inertia tensor.

[0027] ii) Grid speed update

[0028] First, the internal force on the grid point i is calculated according to the deformation gradient F of the surrounding particles:

[0029]

[0030] Then update the grid velocity

[0031]

[0032] ⅰii) Grid-to-Particle Information Transfer (G2P)

[0033] The grid information is transferred to the particles in the following way to ensure energy conservation:

[0034]

[0035] Particles will obtain velocity from compatible grid points and the normal component of velocity from incompatible grid points to achieve automatic MPM fluid-structure interaction without penetration.

[0036] c) Update strain and particle movement

[0037] Update the strain using the particle deformation gradient:

[0038]

[0039] in is the particle deformation gradient at the previous moment, F p is the deformation gradient of the updated particle, I is the identity matrix, is the calculated particle velocity at the next moment, and Δt is the time interval.

[0040] Then, the particle position at the current moment is obtained through the newly calculated particle velocity:

[0041]

[0042] After obtaining the final particle position of each frame, the particle surface can be reconstructed through the OpenVDB library and rendered to generate fluid-solid interaction animation effects.

[0043] Beneficial effects of the present invention:

[0044] The present invention effectively reduces the numerical viscosity of the hybrid particle grid method with relatively small performance loss, so that the fluid and solid in the fluid-solid coupling simulation animation can be naturally separated after contact, which is more realistic and in line with the laws of physics, and can be applied in the fields of realistic film and television special effects, animation, games, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0046] Figure 2 It is a schematic diagram of the process of simulating the sand flow impacting the jelly with different material parameters in the present invention;

[0047] Figure 3 This is a schematic diagram of the present invention simulating the process of toy ducks of different densities falling into water;

[0048] Figure 4 A schematic diagram of the present invention simulating the process of a dam breaking and impacting a bear doll;

[0049] Figure 5 A comparison diagram of the traditional MPM method and the method of the present invention in simulating fluid impact on a fixed rabbit toy;

[0050] Figure 6 It is a comparison diagram of simulating fluid falling on a small ball using the traditional MPM method, the signed distance field method and the method of the present invention. DETAILED DESCRIPTION

[0051] The present invention is described in detail below with reference to the accompanying drawings:

[0052] The present invention comprises the following steps:

[0053] 1) Fluid-solid boundary information collection based on particle grid transmission

[0054] The particle and grid normals are estimated using mass gradients, and then the compatibility of the grid and particles is calculated, and the normal and compatibility information is recorded for use in subsequent steps.

[0055] 2) Use the decomposition compatible affine particle mesh transfer algorithm to transfer information from particles to meshes. Use the normal and compatibility information recorded in the previous step to transfer the mass, velocity and other properties carried by the particles to the grid points according to the decomposition compatible affine particle mesh transfer algorithm, and ensure the conservation of momentum.

[0056] 3) Grid speed update

[0057] According to the deformation gradient of particles around each grid point, the internal force on the grid point is calculated, and the grid point velocity is updated according to Newton's second law.

[0058] 4) Use the decomposition compatible affine particle mesh transfer algorithm to transfer information from the grid to the particle. Use the normal and compatibility information recorded in the first step to transfer the grid point velocity to the particle according to the decomposition compatible affine particle mesh transfer algorithm, and ensure the conservation of momentum.

[0059] 5) Update strain and particle movement

[0060] The particle deformation gradient is updated through the velocity gradient; the particle position at the current moment is explicitly updated through the newly calculated particle velocity.

[0061] The steps of collecting fluid-solid boundary information of the present invention are specifically as follows:

[0062] First, the mass of the solid grid and the normal of the solid particle are calculated by transferring the particle to the grid:

[0063]

[0064] The superscript s indicates solid, m p is the particle mass, m i is the grid mass, w ip is the B-spline interpolation weight of grid point i and particle p, n p is the particle's normal, is the gradient operator;

[0065] Next, calculate the grid point normal and fluid particle normal

[0066]

[0067] where n i is the grid point normal, is the fluid particle normal.

[0068] Then estimate the particle phase field gradient and the material-weighted particle phase field gradient Q p :

[0069]

[0070] where sp represents the fluid-solid phase field of the particle, s i represents the grid point flow-solid phase field, both of which are 1 for fluid and 0 for solid. Then calculate the exact grid point flow-solid phase field value s i :

[0071]

[0072] Finally, the compatibility c between the grid point i and the particle p is calculated ip , if and only if s i =s p When c ip is 1.

[0073] The decomposition compatibility affine particle mesh transmission steps described in the present invention are specifically as follows:

[0074] First, particle-to-grid information transmission (P2G) is performed to transfer the particle information to the grid points according to the following method to ensure energy conservation:

[0075]

[0076] v i =(m i v i ) norm / m i +(m i v i ) tan / m i+

[0077] where p i+ represents the particle with the same compatibility as grid point i, p i- represents particles with different compatibility with grid point i; i p+ represents the grid point with the same compatibility as particle p, i p- represents a grid point with different compatibility with particle p, B q is the affine state matrix, D q is the inertia tensor.

[0078] Then grid-to-particle information transfer (G2P) is performed

[0079] The grid information is transferred to the particles in the following way to ensure energy conservation:

[0080]

[0081] Particles will obtain velocity from compatible grid points and the normal component of velocity from incompatible grid points to achieve automatic MPM fluid-structure interaction without penetration.

[0082] The specific implementation process of the present invention is:

[0083] like Figure 1 As shown in the figure, firstly, the fluid-solid boundary information is collected through a particle mesh transmission to obtain the boundary normal and compatibility, then the particle-to-mesh information transmission based on the decomposition compatibility affine particle mesh transmission algorithm is performed, then the grid velocity is updated through the deformation gradient, then the mesh-to-particle information transmission based on the decomposition compatibility affine particle mesh transmission algorithm is performed, and finally the position is updated through the particle velocity. The whole process can complete the simulation from the current frame to the next frame, and after rendering, an animation effect of fluid and solid coupling that conforms to the real scene can be obtained.

[0084] The present invention performs fluid-solid coupling simulation based on the MPM particle grid hybrid method and the decomposition compatibility affine particle grid algorithm, and the effect is shown as follows:

[0085] Figure 2 The effect of three sand particles of the same shape falling on jellies with different Young's moduli is shown. A total of 477,234 particles are used in this scene. From left to right, the Young's modulus of each column of jellies is 1000, 2000 and 4000 respectively. The upper and lower rows are the 80th and 160th frames of the simulation respectively. It can be intuitively seen from the figure that the present invention can correctly handle the boundary conditions of fluid-solid coupling, and the particle flow and jellies can be naturally separated in the end, while retaining the shaping material of the sand.

[0086] Figure 3 The scene shows the effect of three rubber toy ducks of different densities falling into the water. A total of 91,245 particles are used in this scene. In the first picture, the density ratios of the duck and water are 0.5, 1, and 2 from left to right. Ducks with a density less than that of water will eventually float on the water, while ducks with a density greater than that of water will eventually sink to the bottom, and ducks with a density similar to that of water will float in the water. This scene shows that the present invention can correctly handle the buoyancy phenomenon of different fluid-solid density ratios under fluid-solid coupling, and it conforms to the laws of physics.

[0087] Figure 4 The effect of a rectangular water body bursting and hitting a bear toy is shown. A total of 1,211,592 particles are used in this scene. The four pictures from top to bottom and from left to right are the effects of the 0th, 60th, 120th, and 240th frames respectively. After the water body hits the bear, the fluid and the solid can couple in both directions to produce a physical effect that conforms to the real scene. The water body is hit and splashes, and the solid is pushed by the water flow. And because the particle grid transmitter of the present invention effectively reduces numerical dissipation, no water droplets remain on the solid surface.

[0088] Figure 5The effect of sand particles falling on a fixed rubber rabbit is shown. A total of 912,935 particles are used in this scene, and each column from left to right shows the effects of the 0th, 30th, 60th, 90th, and 150th frames. The first row shows the effect of the traditional MPM method, and the second row shows the effect of the decomposition-compatible affine particle mesh algorithm of the present invention. As can be seen from the figure, the method of the present invention effectively reduces the numerical viscosity of the traditional MPM, allowing the fluid and solid to be separated naturally.

[0089] Figure 6 The effect of fluid falling on three small balls in a two-dimensional scene is demonstrated. A total of 85,245 particles are used in this scene. The first line is a decomposed compatibility affine particle mesh algorithm that uses a signed distance field for compatibility judgment, the second line is a traditional MPM method, and the third line is a decomposed compatibility affine particle mesh algorithm that uses a phase field gradient for compatibility judgment. The traditional MPM method obviously has fluid-solid viscosity problems that do not conform to physical laws; and the decomposed compatibility affine particle mesh algorithm for compatibility judgment can reduce non-physical viscosity. In the selection of methods for judging compatibility, the effects of using a signed distance field and a phase field gradient are similar, and both are more in line with real scenes, but the phase field gradient method proposed in the present invention is 2.7 times faster than the traditional signed distance field that is more commonly used.

[0090] The above examples are only specific embodiments of the present invention. Obviously, the present invention is not limited to the above examples, and many variations are possible. All variations that can be directly derived or associated with the contents disclosed by a person skilled in the art should be considered as the protection scope of the present invention.

Claims

1. A solid-liquid coupling simulation method based on decomposition compatible affine particle mesh algorithm, characterized in that: The method comprises the following steps: a) Fluid-solid boundary information collection based on particle grid transmission i) Using mass gradients to estimate particle and grid normals First, the mass of the solid grid and the normal of the solid particle are calculated by transferring the particle to the grid: The superscript s indicates solid, m p is the particle mass, m i is the grid mass, w ip is the B-spline interpolation weight of grid point i and particle p, np is the normal of the particle, is the gradient operator; Then calculate the grid point normals and fluid particle normals: where ni is the grid point normal, is the fluid particle normal; ii) Computing the compatibility of grid points and particles First, estimate the particle phase field gradient And the material-weighted particle phase field gradient Qp: Where sp represents the fluid-solid phase field of the particle, and si represents the fluid-solid phase field of the grid point, both of which are 1 for fluid and 0 for solid; Then the exact grid flow solid phase field value si is calculated: Finally, the compatibility c between the grid point i and the particle p is calculated ip , if and only if s i =s p When c ip is 1; b) Use the decomposition-compatible affine particle-mesh transfer algorithm to transfer information between particles and meshes i) Particle-to-Grid Information Transfer (P2G) The particle information is transferred to the grid points in the following way to ensure energy conservation: in i =(m i in i ) norm / m i +(m i in i ) tan / m i+ where p i+ represents the particle with the same compatibility as grid point i, p i- represents particles with different compatibility with grid point i; i p+ represents the grid point with the same compatibility as particle p, i p- represents a grid point with different compatibility with particle p, B q is the affine state matrix, D q is the inertia tensor; ii) Grid speed update First, the internal force on the grid point i is calculated according to the deformation gradient F of the surrounding particles: Then update the grid velocity ⅰii) Grid-to-Particle Information Transfer (G2P) The grid information is transferred to the particles in the following way to ensure energy conservation: The particles will obtain the velocity from the compatible grid points and the normal component of the velocity from the incompatible grid points to achieve automatic MPM fluid-structure interaction without penetration; c) Update strain and particle movement Update the strain using the particle deformation gradient: in is the particle deformation gradient at the previous moment, F p is the deformation gradient of the updated particle, I is the identity matrix, is the particle velocity at the next moment that has been calculated, and Δt is the time interval; Then, the particle position at the current moment is obtained through the newly calculated particle velocity: After obtaining the final particle position of each frame, the particle surface is reconstructed through the Marching Cubes algorithm, and the fluid-solid coupling animation effect is rendered.

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