CN115310339A - Solid-liquid coupling simulation method with surface tension effect based on material point method - Google Patents
Solid-liquid coupling simulation method with surface tension effect based on material point method Download PDFInfo
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Abstract
The invention discloses a solid-liquid coupling simulation method with a surface tension effect based on a material dot method, which belongs to the field of computer graphics and physics-based simulation, wherein a system used by the simulation method comprises solid model modeling, fluid model modeling, level Set implicit surface construction, marching cube display surface construction, surface particle resampling and collision detection; the system simulates fluid and solid on the basis of a material point method, resamples fluid surface particles by constructing Level Set, and adds surface tension to the fluid by using a CSF model; different background grids are used for respectively simulating fluid and solid so as to solve the inherent adhesion phenomenon during the solid-liquid coupling of the MPM and realize the sliding contact effect during the solid-liquid coupling; finally, the coupling phenomenon of the incompressible fluid with the surface tension effect and the nonlinear elastic solid is realized.
Description
Technical Field
The invention relates to the field of computer graphics and physics-based simulation, in particular to a solid-liquid coupling simulation method with a surface tension effect based on a material point method.
Background
Surface tension is very important for free surface fluids, and how to more realistically simulate fluids with surface tension is also a hot spot of research in the field of graphics in recent years.
In the prior art, some extend the GEM method to the treatment of incompressible fluids, where the effect of surface tension is added; some display boundary conditions are surface tension in the projection step, and a Level Set surface is used to simulate the contact angle of a water drop, however, when the surface tension effect dominates the scene, the explicit surface tension calculation can cause the instability of the system, such as the simulation of a bubble; some use a semi-implicit method based on CSF model to calculate surface tension; some proposed semi-implicit surface tension calculation methods based on Level Set utilize the divergence of the velocity field of the fluid surface as the surface curvature of the fluid to simulate more real bubbles; some of them use a significantly different method, by solving a volume conservation equation based on mean curvature instead of deriving the surface tension formula, the lagrangian surface tension calculation is usually display geometry discretization compared to the grid-based calculation method; some use the deformation operator to simulate the liquid drop on the surface mesh; some simulation complex bubble structures use a non-flow Lagrange triangular mesh to integrate surface tension information to a mesh vertex; there have been proposed surface-only fluidic frameworks that apply a general three-dimensional fluidic solver to the surface mesh. Lagrange surface tension calculation can also be implicitly processed; some hybrid frameworks are provided, implicit surface tension is calculated under a Lagrange grid, and pressure solution is carried out on a background grid; there are lagrangian equations using incompressible fluids that deal with the specific surface tension in a completely implicit way. There is proposed a new three-term coupling method for simulating the interaction between solid and fluid driven by strong surface tension.
The commonly used solid-liquid coupling solver is usually used for simulating a fluid by using an Euler method, and is used for simulating a solid by using a Lagrange method, and the coupling between the Euler method and the Lagrange method is usually used for using the speed of the solid as a boundary condition of the fluid.
In the prior art, some methods take a related contact surface as interaction, and respectively solve a fluid and a solid on the contact surface; some use similar methods, but use the predicted solid position as the speed limit of the fluid projection step, and this weak coupling method usually has a certain limit in accuracy and stability, and these problems can be solved by using an overall strong coupling method, i.e. putting the fluid and the solid into the same linear system to solve; the first completely implicit stable solid-fluid two-way coupling solver is proposed in the literature, and integrates a fluid pressure projection equation and a speed updating equation of a deformation body into an asymmetric linear equation set; some propose a positive definite symmetry equation set, solve the coupling of the fluid and rigid body by making the kinetic energy minimize; some use algebraic transformation to further modify the above positive definite symmetry equations; some incompressible fluid and rigid body bidirectional coupling solvers based on multiple grids are provided, and the method can solve the solid-liquid coupling system more efficiently; some achieve solid coupling of the fluid to the subgrid; there has been proposed a method of bi-directional coupling of a non-viscous non-linear elastic solid with an incompressible fluid.
The MPM method has been introduced into the field of graphics, and is capable of automatically supporting mesh-based collision processing and bidirectional coupling interaction, but has a non-slip boundary condition at a collision contact surface.
In the prior art, some methods for transmitting APICs are provided, which can better ensure the conservation of angular momentum of the system. Some uses MPM to truly simulate hair; there have been proposals to use MPM to simulate viscoelastic fluids, foams and sponges; some use accurate frictional contact calculation to couple the MPM to the rigid body; some extend the MPM method to simulate sand; some proposed generalized interpolation material point methods adaptively subdivide a specific area; some use anisotropic resistance in a separate velocity grid enables more flexible fluid-cloth interaction.
As can be seen from the above prior arts, in the conventional surface tension effect simulation method, most studies are performed by only simulating the addition of surface tension to a single fluid or only adding a non-slip boundary condition for solid-liquid coupling, but neglecting the surface tension effect during solid-liquid interaction.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a solid-liquid coupling simulation method with a surface tension effect based on a material point method, which simulates fluid on the basis of the material point method, resamples fluid surface particles by constructing Level Set, adds the surface tension to the fluid by using a CSF model, and simulates the fluid and the solid respectively by using different background grids so as to solve the inherent adhesion phenomenon in the MPM solid-liquid coupling, realize the sliding contact effect in the solid-liquid coupling and finally realize the coupling phenomenon of an incompressible fluid with the surface tension effect and a nonlinear elastic solid.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a solid-liquid coupling simulation method with surface tension effect based on a material dot method comprises the following steps:
step 1, creating MPM fluid particles and solid particles, initializing, and storing physical quantities on the fluid particles and the solid particles;
step 2, constructing an implicit Level Set curved surface of the fluid, constructing a spherical Level Set surface for each fluid particle, generating a symbol distance field, and combining each spherical Level Set into the implicit curved surface of the whole fluid simulation area;
step 3, calculating a gradient field and a Laplace calculation sub-field of the fluid region by using the symbol distance field;
step 4, converting the implicit curved surface into a Marking Cubes display curved surface, and using a zero equipotential surface of the symbolic distance field as an equipotential surface for constructing the Marking Cubes;
5, resampling the surface particles on the display curved surface, wherein the generated surface particles only have position information and do not have mass and speed physical quantities, and the surface particles are generated at the beginning of each time step and deleted at the end of each time step;
step 6, carrying out grid marking;
step 7, calculating the surface tension on the surface particles;
step 8, mapping the surface tension on the surface particles to the fluid particles;
step 9, mapping the particle information to a background grid, wherein the momentum and the quality of the MPM particles are mapped to the background grid by using a standard APIC mapping mode;
step 10, adding an external force on the background grid, and solving a new speed;
step 11, impulse collision processing, namely calculating the speed of the fluid after collision by using an impulse mode to generate an impact effect, and adding a proper amount of speed attenuation to the fluid in the tangential direction of a solid-liquid contact surface;
and step 12, mapping the information on the background grid back to the MPM particles, transmitting the particle speed on the background grid back to the MPM particles by using a standard APIC mapping mode, and updating the affine speed of the MPM particles.
The technical scheme of the invention is further improved as follows: in step 1, the physical quantity includes position, speed, deformation gradient, affine speed, and quality.
The technical scheme of the invention is further improved as follows: in step 2, constructing an implicit Level Set curved surface:
constructing a spherical Level Set surface for each fluid particle, wherein the expression of the Level Set is as follows:
f(x)＝|x-c|-r (1)
in the formula, x represents the position of the particle, r represents the radius of the spherical Level Set, and c represents the position of the liquid particle.
The technical scheme of the invention is further improved as follows: in step 3, the gradient field of the fluid region represents a normal vector field of the fluid, and the laplacian operator field represents a curvature field of the fluid.
The technical scheme of the invention is further improved as follows: in step 6, fluid particle grids, fluid surface grids, solid particle grids, solid surface grids, air grids and fluid-solid contact grids are marked respectively.
The technical scheme of the invention is further improved as follows: in step 7, in order to calculate the surface tension more accurately, the calculation is performed only on the fluid free surface mesh, and the surface tension calculation is not performed on the fluid surface of the solid-liquid contact surface.
The technical scheme of the invention is further improved as follows: in step 8, the surface tension calculated at the surface particle is transmitted to the fluid background grid through a B-spline difference function, and then transmitted to the fluid surface particle from the fluid background grid.
The technical scheme of the invention is further improved as follows: in the fluid surface tension calculation mode in the steps 7 and 8, a gradient field of a symbol distance field is used as a normal vector field of the fluid, a Laplace operator field of the symbol distance field is used as a curvature field, a bilinear difference function is used for calculating a normal vector and a curvature of the position of the resampled surface particle, and then the surface tension is calculated at the surface particle; after the surface tension is calculated at the surface particles, the calculated surface tension is transmitted to a background grid through a bilinear difference function and then transmitted to the surface fluid particles; use of
Representing the free surface of the fluid or the portion of the fluid affected by surface tension at time t.
The technical scheme of the invention is further improved as follows: in step 12, the solid-liquid coupling treatment method needs to ensure that the normal phase velocity of the fluid is consistent with the normal velocity of the solid in order to prevent the fluid from bouncing off; after solid-liquid contact, the speeds were:
in the formula, v r Is the relative velocity of the fluid and the solid,
the velocity of the fluid at the solid-liquid interface, n i Is in the normal vector direction of the solid-liquid contact surface;
in the formula (I), the compound is shown in the specification,
the solid velocity of the solid-liquid contact surface.
Due to the adoption of the technical scheme, the invention has the technical progress that:
1. the invention provides a method for coupling fluid and solid with surface tension effect under the condition of a slippage boundary, which is different from the traditional method for completely separating the solid from the liquid during solid-liquid coupling, and more truly simulates the solid-liquid coupling.
2. The invention solves the adhesion problem of the solid-liquid contact surface inherent in the traditional MPM, and more accurately solves the adhesion problem generated when the fluid is coupled with the solid.
3. The invention aims at the traditional method that the surface tension of the fluid surface is completely calculated, and the calculation mode of the surface tension of the fluid in the solid-liquid contact surface is more accurately processed through grid marking.
Drawings
FIG. 1 is a flow chart of a simulation process in an embodiment of the present invention;
FIG. 2 is a diagram of a surface particle resampling process according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating a process of calculating surface tension according to an embodiment of the present invention;
FIG. 4 is a surface tension grid marking diagram in accordance with an embodiment of the present invention;
FIG. 5 is a graph showing the experimental results in the example of the present invention.
Detailed Description
The embodiment of the application provides a solid-liquid coupling simulation method with a surface tension effect based on a material point method, solves the inherent solid-liquid contact surface attachment problem of MPM in the prior art, more accurately solves the adhesion phenomenon problem generated when fluid is coupled with solid, more accurately solves the fluid surface tension calculation problem under the condition of a slippage boundary, simulates fluid and solid on the basis of the material point method, resamples fluid surface particles by constructing Level Set, determines the free surface of the fluid by using a grid marking method, and adds surface tension to the fluid by using a CSF model to solve the fluid surface tension calculation problem under the condition of the slippage boundary; different background grids are used for respectively simulating fluid and solid so as to solve the inherent adhesion phenomenon during the solid-liquid coupling of the MPM and realize the sliding contact effect during the solid-liquid coupling; finally, the coupling phenomenon of the incompressible fluid with the surface tension effect and the nonlinear elastic solid is realized, so that more real simulation and animation design effects can be obtained.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Moreover, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
MPM is an abbreviation for the Material Point Method, translated in Chinese as: a material dot method;
CSF is an abbreviation for The continuous Surface Force Model;
the invention is further described in detail below with reference to the drawings and examples:
the system comprises solid model modeling, fluid model modeling, level Set implicit surface construction, marching Cubes display surface construction, surface particle resampling, collision detection and the like.
(1) Solid model modeling is performed by voxelizing the obj model as a discrete point model. In order to build the MPM solid particles and initialize their positions.
(2) Fluid model modeling is used to initialize MPM fluid particles.
(3) Level Set implicit surfaces build implicit surfaces for building fluids. Because different Level sets can be combined, a spherical Level Set implicit surface is created around each fluid particle, and the spherical implicit surfaces are combined to form a symbolic distance field representing the entire simulation region
The portion being the fluid surface.
(4) Marching Cubes show surfaces build up a show surface for building fluids. Distance fields generated using implicit surfaces, where the display surface and the implicit surface are interconvertible
And converting the surface into an explicit Marching Cubes surface for resampling surface particles.
(5) Surface particle resampling is used to generate surface particles without mass, on which the surface tension of the fluid is calculated using a CSF model.
(6) The collision detection uses an impulse manner to perform collision velocity processing to solve the problem of viscosity inherent in the MPM.
As shown in fig. 1, the solid-liquid coupling simulation method with surface tension effect based on the material point method specifically includes:
1. constructing an implicit Level Set curved surface:
constructing a spherical Level Set surface for each fluid particle, wherein the expression of the Level Set is as follows:
f(x)＝|x-c|-r (1)
in the formula, x represents the position of the particle, r represents the radius of a spherical Level Set, and c represents the position of the liquid particle;
using equation (1), the Symbol Distance Field (SDF) for each fluid particle can be calculated, and the different symbol distance fields are combined to a minimum value to obtain the wholeSymbolic distance field of a fluid region
2. Resampling fluid surface particles:
first, an explicit surface is generated using the symbolic distance field zero equipotential surface of the fluid region as the iso-surface for generating Marching Cubes, and the generated display surface is resampled to surface particles, the generated particle positions are the fluid surface particle positions, and the resampled surface particles are represented by x q It is shown that the particle resampling process is as shown in fig. 2.
3. And (3) calculating the surface tension:
the calculation of the surface tension is performed on surface particles, and the surface tension is calculated on the sampled surface particles using a CSF model expressed as:
where α is the surface tension coefficient of the fluid, κ is the average curvature of the fluid surface, n is the unit normal vector at the fluid surface,
is the surface gradient.
The first part of equation (2) acts in the normal direction and generates a force that affects the change in the surface area of the fluid by local curvature. The second portion acts in a tangential direction to the surface, causing the fluid particles to flow from a location of low surface tension to a location of high surface tension. If the surface tension coefficient α is constant, the tangential component is zero.
The gradient field of the symbol distance field can be taken as the normal vector field of the fluid and the laplacian field of the symbol distance field can be taken as the curvature field, thereby calculating the surface tension at the surface particles. After calculating the surface tension at the surface particle, the calculated surface tension is transferred to the background mesh and then to the surface fluid particle by a difference function, as shown in fig. 3.
More accurate calculations are made at the solid-fluid interface while supporting dynamic solid-to-fluid coupling. As shown in fig. 3, the left diagram shows a solid-liquid coupling system with a free-sliding boundary condition.
Storing symbolic distance fields using a Cartesian grid
Then it can pass through
Calculating the curvature field of the simulation region, the normal vector field and the curvature field
Normal vector field
Using a bilinear difference function delta i (x) Representing a bilinear interpolation function at a grid node i, using the interpolation function delta for the surface particle and Cartesian background grids i (x) In correlation, the curvature at the surface particle location can be calculated as well as the normal vector. Use of
Representing the free surface of the fluid or the fraction of the fluid affected by the surface tension at time t, the grid marks are shown in fig. 4, and the surface tension of the surface particles can be expressed as:
wherein alpha is the surface tension coefficient of the fluid,
representing the curvature at mesh node i at time step n,
representing the normal vector at mesh node i at time step n,
the position of the surface particle q at time step n is shown.
4. Simulation method based on MPM
4.1 constitutive model
In material mechanics, a constitutive model is a physical model for expressing constitutive relation of materials, each particle is regarded as one part of the material by an MPM algorithm, the energy of each part of the material is calculated by using an energy density function, and the potential energy of the whole material can be obtained by integrating the potential energy carried by each part of the material.
The movement of the material can be represented as a mapping description with an initial region of material Ω 0 The spatial region of the material at time t is denoted as Ω t 。X∈Ω 0 Denotes the position of the material particle at the initial time, x ∈ Ω t Representing the position of the material particle at time t, the expression for the deformation map can be expressed as phi: (·, t): omega 0 →Ω t ,
d＝2,3。
Through the mapping function, the calculation formula of the deformation gradient F can be obtained as follows:
the deformation gradient can be used to quantify the local deformation of the material, and the value of the deformation gradient determinant is obtained by J = det (F), and the value of J represents the volume change of one material point.
Each particle in the MPM represents a portion of a material, and the cauchy stress is defined as an energy density function of the superelastic body, defined as:
where P is pressure and Ψ is an energy density function.
Calculating by using a fixed-corotated constitutive model, wherein the expression of the energy density function is as follows:
wherein F is deformation gradient, J is deformation gradient determinant value, lambda and mu are lamee parameters which represent resistance of the material to deformation and volume change, and sigma i The characteristic value of the deformation gradient F is obtained by carrying out SVD on the deformation gradient F.
4.2 interpolation function
With N i (x) Representing B spline difference function at node i of the grid, and passing the particles and the grid through interpolation function N i (x) The correlation, which determines the strength of the interaction between the particle and the grid. The weight is larger if the distance between the particle and the grid is closer, whereas the weight is smaller if the distance is farther.
Interpolation function N i (x) The expression of (a) is:
4.3 mapping particle carried information to background grid
Momentum and mass are transferred from the particles to the background grid using standard APIC mapping approaches.
In the formula (I), the compound is shown in the specification,m p is the mass of the particles p and,
for the time step n the position of the particle p,
the quality of the storage for the mesh node i,
is the velocity of the particle p at time step n,
stored speed, x, for time step n grid node i i To be the location of the mesh node i,
the affine velocity of the particle p at time step n.
Here, the surface tension calculated at the surface particle is also transmitted to the background mesh using B-spline difference functions.
In the formula (I), the compound is shown in the specification,
is the surface tension at the surface particle q at time step n.
4.4 grid solving
The total potential energy of the MPM simulation material can be expressed by an energy density function ψ, and by integrating the energy of all MPM particles, it can be obtained:
in the formula (I), the compound is shown in the specification,
is a materialThe volume of the material, e is the total energy of the material, and the elastic force of the material is the negative gradient of the total potential energy of the material at the position thereof, so that all stress conditions of the material can be calculated in the background grid as follows:
according to the momentum theorem, the change of the momentum on the grid nodes is as follows:
4.5 mapping background grid information to particles
After updating the velocity of the grid, the velocity on the grid is also transferred back to the particle using APIC and the affine velocity of the particle is updated.
5. Solid-liquid coupling
In order to solve the inherent adhesion problem of MPM during solid-liquid interaction, different grids are used for respectively simulating a solid and a fluid, iteration is respectively carried out between the solid and the fluid, and the solid-liquid coupling contact surface is treated by using impulse effect, so that the coupling of the fluid and an elastomer is better treated, and the adhesion problem is solved.
The impact is treated by impulse, and the impact effect of liquid on solid can be generated when the impact is performed. In order to ensure that the fluid is not separated due to impulse calculation in collision, the normal speed of the fluid is ensured to be consistent with that of the solid at the contact surface instead of directly adding impulse effect, so that the fluid is flicked. The velocity of the fluid relative to the solid is first calculated:
in the formula (I), the compound is shown in the specification,
is the velocity of the fluid at the solid-liquid contact surface,
the solid velocity of the solid-liquid contact surface.
Using the gradient of the previously generated symbol distance field to calculate the fluid surface normal vector and the tangential velocity of the fluid relative to the solid surface:
the grid impulse calculation expression during solid-liquid coupling is as follows:
calculating friction force by using a coulomb friction model, recording the coefficient of dynamic friction as mu, and when an impulse effect is applied, the maximum value of the change of the allowed tangential speed of the coulomb friction is
To prevent the separation of the fluid from the contact surface due to impulse calculations, the normal velocity of the fluid is guaranteed to coincide with the normal velocity of the solid, preventing the fluid from bouncing off. Therefore, after solid-liquid contact, the speeds are:
in the formula, v r Is the relative velocity of the fluid and the solid,
the velocity of the fluid at the solid-liquid interface, n i Is in the direction of the normal vector of the solid-liquid contact surface.
In the formula (I), the compound is shown in the specification,
the solid velocity of the solid-liquid contact surface.
The results of the experiment are shown in FIG. 5.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (9)
1. A solid-liquid coupling simulation method with surface tension effect based on a material point method is characterized in that: the method comprises the following steps:
step 1, creating MPM fluid particles and solid particles, initializing, and storing physical quantities on the fluid particles and the solid particles;
step 2, constructing an implicit Level Set curved surface of the fluid, constructing a spherical Level Set surface for each fluid particle, generating a symbol distance field, and combining each spherical Level Set into an implicit curved surface of the whole fluid simulation area;
step 3, calculating a gradient field and a Laplace calculation sub-field of the fluid region by using the symbol distance field;
step 4, converting the implicit curved surface into a Marching Cubes display curved surface, and using a zero equipotential surface of the symbolic distance field as an equipotential surface for constructing the Marching Cubes;
5, resampling the surface particles on the display curved surface, wherein the generated surface particles only have position information and do not have quality and speed physical quantities, and the surface particles are generated at the beginning of each time step and deleted at the end of each time step;
step 6, carrying out grid marking;
step 7, calculating the surface tension on the surface particles;
step 8, mapping the surface tension on the surface particles to the fluid particles;
step 9, mapping the particle information to a background grid, wherein the momentum and the quality of the MPM particles are mapped to the background grid by using a standard APIC mapping mode;
step 10, adding an external force on the background grid, and solving a new speed;
step 11, impulse collision processing, namely calculating the speed of the fluid after collision by using an impulse mode to generate an impact effect, and adding a proper amount of speed attenuation for the fluid in the tangential direction of a solid-liquid contact surface;
and step 12, mapping the information on the background grid back to the MPM particles, transmitting the velocity of the particles on the background grid back to the MPM particles by using a standard APIC mapping mode, and updating the affine velocity of the MPM particles.
2. The solid-liquid coupling simulation method with surface tension effect based on the material point method as claimed in claim 1, wherein: in step 1, the physical quantity includes position, speed, deformation gradient, affine speed, and quality.
3. The solid-liquid coupling simulation method with surface tension effect based on the particle method of claim 1, wherein: in step 2, constructing an implicit Level Set curved surface:
constructing a spherical Level Set surface for each fluid particle, wherein the expression of the Level Set is as follows:
f(x)＝|x-c|-r (1)
in the formula, x represents the position of the particle, r represents the radius of the spherical Level Set, and c represents the position of the liquid particle.
4. The solid-liquid coupling simulation method with surface tension effect based on the material point method as claimed in claim 1, wherein: in step 3, the gradient field of the fluid region represents a normal vector field of the fluid, and the laplacian field represents a curvature field of the fluid.
5. The solid-liquid coupling simulation method with surface tension effect based on the particle method of claim 1, wherein: in step 6, fluid particle grids, fluid surface grids, solid particle grids, solid surface grids, air grids and fluid-solid contact grids are marked respectively.
6. The solid-liquid coupling simulation method with surface tension effect based on the material point method as claimed in claim 1, wherein: in step 7, in order to calculate the surface tension more accurately, the calculation is performed only on the fluid free surface mesh, and the surface tension calculation is not performed on the fluid surface of the solid-liquid contact surface.
7. The solid-liquid coupling simulation method with surface tension effect based on the particle method of claim 1, wherein: in step 8, the surface tension calculated at the surface particle is transmitted to the fluid background grid through a B-spline difference function, and then transmitted to the fluid surface particle from the fluid background grid.
8. The solid-liquid coupling simulation method with surface tension effect based on the material point method as claimed in claim 1, wherein: in step 7 and step 8, in a fluid surface tension calculation mode, a gradient field of a symbol distance field is used as a normal vector field of the fluid, a Laplace operator field of the symbol distance field is used as a curvature field, a bilinear difference function is used for calculating a normal vector and a curvature of the position of the resampled surface particle, and further surface tension is calculated at the surface particle; at the surface particleAfter the surface tension, transmitting the calculated surface tension to a background grid through a bilinear difference function, and then transmitting the surface tension to surface fluid particles; use of
Representing the free surface of the fluid or the portion of the fluid affected by surface tension at time t.
9. The solid-liquid coupling simulation method with surface tension effect based on the particle method of claim 1, wherein: in step 12, the solid-liquid coupling treatment method needs to ensure that the normal phase velocity of the fluid is consistent with the normal velocity of the solid in order to prevent the fluid from bouncing off; after solid-liquid contact, the speeds were:
in the formula, v r Is the relative velocity of the fluid and the solid,
the velocity of the fluid at the solid-liquid interface, n i Is the normal vector direction of the solid-liquid contact surface;
in the formula (I), the compound is shown in the specification,
the solid velocity of the solid-liquid contact surface.
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| CN116824009A (en) * | 2023-06-29 | 2023-09-29 | 广州市大神文化传播有限公司 | Animation rendering method, system, equipment and storage medium |
| CN116824009B (en) * | 2023-06-29 | 2024-03-26 | 广州市大神文化传播有限公司 | Animation rendering method, system, equipment and storage medium |
| CN118410745A (en) * | 2024-07-04 | 2024-07-30 | 大连海事大学 | Spray simulation method of marine carbon dioxide fire extinguisher |
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