CN103425849A - Simulation method for dynamic barrier to influence lower fluid - Google Patents

Simulation method for dynamic barrier to influence lower fluid Download PDF

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CN103425849A
CN103425849A CN2013103960342A CN201310396034A CN103425849A CN 103425849 A CN103425849 A CN 103425849A CN 2013103960342 A CN2013103960342 A CN 2013103960342A CN 201310396034 A CN201310396034 A CN 201310396034A CN 103425849 A CN103425849 A CN 103425849A
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barrier
texture
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CN103425849B (en
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卢光辉
李朋
陈雷霆
蔡洪斌
曹跃
邱航
崔金钟
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University of Electronic Science and Technology of China
Institute of Electronic and Information Engineering of Dongguan UESTC
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University of Electronic Science and Technology of China
Institute of Electronic and Information Engineering of Dongguan UESTC
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Abstract

The invention relates to a simulation technology imitating a dynamic barrier to influence lower fluid behaviors on the basis of a physical mode. The technology comprises the steps of sequentially calculating the convective term, the outer force term and the pressure term in a hydrodynamic equation (Navier-Storkes equation); upgrading physical quantities, such as speed and pressure, of fluid; finishing the simulation calculation of the fluid. When the pressure term is calculated, mutual influence of the fluid and the barrier is considered, and a coupled linear equation between the fluid and the barrier is set up according to the Lagrange's equation of motion of the barrier and the uncompressed conditions of the fluid. The pressure term is upgraded through solving the linear equation. Due to the fact that the simulation calculation of the fluid is realized in a GPU, and the simulation of the barrier is executed in a CPU, in order to make the fluid to be coupled with the barrier, a voxelization process is conducted on the dynamic barrier in the simulation process according to the simulation technology, the dynamic barrier is is mapped onto a simulation grid of the fluid, and the calculation of fluid pressure is finished through the combination of the CPU and the GPU.

Description

The emulation mode of the lower fluid of a kind of dynamic barrier impact
Technical field
The invention belongs to the virtual reality technology field, relate in particular to combine with the GPU emulation mode of the lower fluid of dynamic barrier based on physics mode impact of CPU.
Background technology
In actual life, about the phenomenon of fluid, can be found everywhere, such as the kitchen smoke risen up slowly, the rivers that flow ahead fast ceaselessly, flame of blazing etc.In fluid, exist various barriers toward the contact meeting, having also has staticly dynamically, and such as free-swimming fish in river, smog passes through forest etc.In spontaneous phenomenon computer simulation field, fluid emulation is one of them important research direction, and it similarly is a kind of useful building puzzle, is the basis of a lot of spontaneous phenomenons of emulation.Yet, due to its huge assessing the cost, it all only belongs to the field that the high-quality off-line is played up all the time.In application in real time, the effect of 3D fluid is all often to depend on particIe system to realize, although particIe system can produce very attractive result, but they also do not meet true outward appearance and the behavior of fluid, the emulation of fluid in real time remains a kind of challenge, especially in fluid, also exists the analogue simulation of various barriers.
Summary of the invention
For the real motion behavior that shows the lower fluid of dynamic barrier impact that can be real-time, the invention provides the emulation mode of the lower fluid of a kind of dynamic barrier impact.The present invention adopts the physical message of 3D texture storage fluid, as speed, pressure etc., uses the 3D texture to make simulation calculation to realize on GPU fully, has improved greatly simulation efficiency.Carry out two in the advection process in the middle of, the semi-Lagrange step adds two-way error compensation and aligning step, and the advection precision is brought up to second order by single order, has reduced the numerical dissipation in the advection process.Improved the method for solving of pressure term in the fluid motion equation, consider influencing each other of fluid and dynamic barrier, dynamic barrier is carried out to voxelization process, be mapped in the fluid grid, set up the coupling linear equation between barrier and fluid according to the lagrange equation of motion of barrier and the incompressibility of fluid, combine with the GPU pressure of Fluid Computation of CPU, synchronously upgrade the motion state of fluid and barrier, improved the authenticity of the lower fluid motion of dynamic barrier impact.When computing velocity divergence and pressure gradient, sampled point is offset in GPU, utilizes the account form of MAC grid to be sampled to the 3D texture, reduced the error in computation process, improved computational accuracy.
The behavior emulation mode of the lower fluid of a kind of dynamic barrier impact of the present invention, the method comprises the following steps:
Step 1, the physical quantity of initialization fluid (as speed, pressure etc.), be stored in the middle of the 3D texture, is convenient to be calculated in GPU.
Step 2, use Semi Lagrangian scheme, the midrange speed field of advection Fluid Computation; For reducing the dissipation in the advection process, obtain higher advection precision, further improve Semi Lagrangian scheme, by semi-Lagrange advection step in the middle of carrying out in advance two, a forward advection and a reverse advection are (, time is contrary), then carry out two-way error compensation and aligning step, obtain more high-precision advection value.
Step 3, all dynamic barriers of voxelization, obtain 3D barrier texture and 3D boundary position texture.When dynamic barrier is carried out to voxelization, can further comprise again:
Step 3.1, utilize the decrement operations that increases progressively of template buffer memory to carry out inside and outside voxelization to all dynamic barriers, and mark barrier unit is SOLID, and element of fluid is FLUID, is saved in 3D barrier texture;
Step 3.2, the barrier model is played up in each grid section one time, in geometric coloration, (Geometry Shader) carries out the crossing operation of cutting into slices with grid to each triangle surface in barrier, use bilinear interpolation to calculate the position of intersecting point coordinate, and unit, corresponding intersection point place is labeled as to BOUNDARY, mean the boundary element of barrier.In pixel coloring device, label information is rendered in the barrier texture, corresponding position of intersecting point is rendered in the boundary position texture.
Step 4, according to 3D barrier texture, dyscalculia thing boundary normal, be kept in 3D boundary normal texture.For boundary element, judge the label information of its neighbours unit according to the barrier texture, normal is calculated in the place adjacent with element of fluid at boundary element, is saved in corresponding boundary normal texture.Wherein, normal direction is pointed to boundary element from element of fluid.
Step 5, read 3D barrier texture, records the index position of obstacles borders in texture.
Step 6, the index position according to obstacles borders in texture, extract boundary position and boundary normal and be saved in corresponding list of locations and normal list.
Step 7, according to the incompressibility of the barrier equation of motion and fluid, set up the coupling linear equation between fluid and barrier.The coupling linear equation of setting up according to the incompressibility of the equation of motion of barrier and fluid is as shown in Equation (1):
（1）
Wherein, For the transition matrix between generalized coordinate system and cartesian coordinate system,
Figure 298686DEST_PATH_IMAGE003
( kThe boundary element number);
Figure 449045DEST_PATH_IMAGE004
Mass matrix for barrier;
Figure 716078DEST_PATH_IMAGE005
For the speed under generalized coordinate before barrier and fluid coupling.
Step 8, CPU is combined with the GPU item, solves the coupling linear equation, the pressure field of Fluid Computation.When solving the coupling linear equation, the method that adopts GPU to combine with CPU, order
Figure 977295DEST_PATH_IMAGE006
,
Figure 380595DEST_PATH_IMAGE007
, first according to the lagrange equation of motion of barrier, in CPU, calculate AWith B, then according to the obstacles borders index, respectively will AWith BWrite in each self-corresponding 3D texture, complete the calculating of terminal pressure in GPU.When Fluid Computation pressure, no matter what solve is coupling linear equation or Poisson equation, all need the divergence of computing velocity in advance.
Step 9, according to the gradient of pressure field, go on the midrange speed field of projection fluid is long without divergence to it, obtains the final speed field of fluid.In this step, need to carry out projection calculating to middle velocity field according to the gradient of pressure field.Adopt MAC grid (a kind of staggered-mesh when computing velocity divergence and pressure gradient, corresponding with central gridding) account form the 3D texture is sampled, being offset separately 0.5 unit on three directions of 3D texture is sampled, can reduce the error in computation process, improve computational accuracy.
The invention has the beneficial effects as follows: the physical message of fluid is kept in the middle of the 3D texture, makes emulation be achieved on GPU, improved simulation efficiency, simultaneously the mutual corresponding simulation calculation process of also having simplified of 3D texture and Eulerian mesh.When computing velocity divergence and pressure gradient, improve the sample mode of 3D texture, on three directions of 3D texture, sampled point has been offset respectively to 0.5 unit, utilized the account form of MAC grid to be sampled to the 3D texture, reduce the error in computation process, improved computational accuracy.Improve the voxelization process of dynamic barrier, add a boundary voxel process, the crossing operation with target slice to each triangle surface execution in barrier in geometric coloration, calculate intersection point (intersection point is the obstacles borders position) by bilinear interpolation, these points are outputed to pixel coloring device, be labeled as BOUNDARY by pixel coloring device and output in the middle of 3D barrier texture, the position of these intersection points is saved in the 3D border texture simultaneously.Because the motion of barrier is simulated in CPU, and the motion of fluid is simulated in GPU, at fluid and barrier, be coupled while calculating, CPU is combined with GPU, according to the resulting boundary information of barrier voxelization, the pressure of boundary is calculated, upgrade the motion state of fluid and barrier by this Simultaneous Pressure, not only improve the efficiency of emulation, also improved the authenticity of the lower fluid motor behavior of barrier impact.
The accompanying drawing explanation
Fig. 1 shows the emulation mode process flow diagram of the lower fluid behavior of a kind of dynamic barrier impact of the present invention.
Fig. 2 shows semi-Lagrange advection method.
Fig. 3 shows the semi-Lagrange advection step after improvement.
Fig. 4 shows advection error analysis and rectification building-out.
Fig. 5 shows the storage mode of MAC grid in the present invention.
Fig. 6 shows the derivation of coupling linear equation between fluid and barrier.
Specific embodiments
Below in conjunction with accompanying drawing and embodiment, the preferential embodiment of the present invention is further illustrated:
Process flow diagram shown in Fig. 1 has provided the detailed process of the whole enforcement of the present invention:
Step 1, the 3D texture of initialization fluid grid establishment and the corresponding equal size of grid, the physical quantity (speed, pressure etc.) of preserving fluid under original state.The 3D texture can be regarded as a kind of array of three-dimensional, for GPU computation process save data, in GPU, by sampling operation, reads the value in texture.
Step 2, the process that is transmitted fluid itself and the physical quantity in fluid by speed is called advection, it is to use Semi Lagrangian scheme that advective term based on GPU calculates, from each grid cell inverse time tracking racetrack, obtain its position in the past, and to the grid cell started, copy the physical quantity (such as speed) of that position, as shown in figure (2), inverse time is followed the trail of velocity field to the X position, value in the grid of the most close X position is carried out to bilinear interpolation, draw required speed, and it is stored in the middle of 3D speed texture.For reducing the numerical dissipation in the advection process, improve the advection precision, the advection process can further be improved, by semi-Lagrange step in the middle of carrying out in advance two, a forward and reverse (that is, the time is contrary).When carrying out Semi Lagrangian scheme, if first carry out a forward carry out again one reverse, must return in theory the initial value before carrying out, yet the calculating of Semi Lagrangian scheme can exist certain error, suppose that this error is e, will produce so the error of 2e with respect to initial value after executing forward and reverse semi-Lagrange,
Figure 639538DEST_PATH_IMAGE008
, can obtain error
Figure 393867DEST_PATH_IMAGE009
.During in the end a step semi-Lagrange advection calculates, two-way error compensation and aligning step, deduct error with currency in advance and carry out the semi-Lagrange advection again, and so operation can reduce the numerical dissipation caused because of error, improves the advection precision.The flow process that whole advection calculates is as shown in figure (3), and the error analysis process is as shown in figure (4).
Step 3, carry out voxelization process to all dynamic barriers, is mapped on the fluid grid, and concrete process is as follows:
Step 3.1, carry out inside and outside voxelization to dynamic barrier.This embodiment adopts rectangular projection that the barrier model of input is played up once in each section of purpose 3D texture structure.When rendering model, utilize the decrement operations that increases progressively of template buffer memory (identical with the dimension of section), the back side increases progressively, and successively decrease in front.So, all voxels that are positioned at model inside will obtain the stencil value of a non-zero, and outside all voxels are still zero.Finally, do once finally traversal, stencil value is copied in the 3D texture, wherein the barrier unit is labeled as SOLID, and element of fluid is labeled as FLUID.
Step 3.2, to the voxelization of dynamic barrier exercise boundary, the boundary position of dyscalculia thing.In this embodiment, the boundary voxel process is similar with inside and outside voxelization, model is played up in each grid section one time, but this time do not use the template buffer memory, but judge the intersection point of each triangle surface with target slice in geometrical processor, bilinear interpolation is calculated position of intersecting point, and this position is boundary position.At pixel coloring device, active cell is labeled as to BOUNDARY and outputs in 3D barrier texture, export the active cell position simultaneously in corresponding 3D border texture.
Step 4, play up the fluid grid one time, judges according to 3D barrier texture whether current cell is boundary element (marking whether as BOUNDARY) in pixel coloring device, dyscalculia thing boundary normal.The computing method of boundary normal are as follows: detecting the neighbours unit of current cell before and after up and down according to 3D barrier texture is barrier unit (SOLID), obstacles borders unit (BOUNDARY) or element of fluid (FLUID).Such as, if its left neighbours (x negative direction) are element of fluid, the normal of active cell points to barrier for the 1(normal direction by fluid on directions X so).Do same operation on other direction, finally normal information is outputed in corresponding 3D boundary normal texture.
Step 5, create the addressable 3D texture of CPU, by the information reproduction in 3D barrier texture in the texture just created.The access texture, record the index of position in the cell place texture that is labeled as BOUNDARY, is saved in the boundary position index.
Step 6, equally create the addressable 3D texture of CPU with step 5, and the information in boundary position texture and boundary normal texture is copied in respective texture respectively.The access texture, the index of trying to achieve according to step 5 reads corresponding boundary position and boundary normal is saved in boundary position list and boundary normal list.
Step 7 is set up the coupling linear equation according to the lagrange equation of motion of barrier and the incompressibility of fluid on normal direction.The lagrange equation of motion of barrier is as shown in Equation (2):
Figure 193196DEST_PATH_IMAGE010
（2）
Wherein,
Figure 716581DEST_PATH_IMAGE011
The mass matrix that means barrier, Mean suffered coriolis force;
Figure 122472DEST_PATH_IMAGE013
With Mean the inside and outside generalized force of barrier.
The incompressibility of fluid, the divergence of fluid velocity field is zero, as shown in Equation (3):
Figure 431279DEST_PATH_IMAGE015
（3）
The process of establishing of coupling linear equation is as shown in figure (6), and the coupling linear equation of foundation is as formula (4)
Shown in:
Figure 766446DEST_PATH_IMAGE016
（4）
Wherein, SBe selection matrix, for selecting the boundary element of barrier, the coupling linear equation is just for boundary element normal direction.
Step 8, the pressure field of Fluid Computation, can be further divided into two kinds of situations.
Situation 1, be labeled as the boundary element of BOUNDARY, on its normal direction by the iterative linear equation calculating pressure that is coupled.Order
Figure 495367DEST_PATH_IMAGE006
,
Figure 574182DEST_PATH_IMAGE007
, according to boundary position and the boundary normal information of barrier, can calculate easily AWith B, then will AWith BValue be filled in the middle of the 3D texture, carry out calculation of pressure in pixel coloring device.If the normal direction of boundary element is the positive dirction towards X, first divergence to be carried out in formula (4) equal sign the right and calculate, the divergence account form as shown in Equation (5), is then calculated the force value of active cell according to formula (6).
Figure 140336DEST_PATH_IMAGE017
（5）
Figure 646403DEST_PATH_IMAGE018
（6）
Situation 2, be labeled as on the tangential direction of BOUNDARY and the element of fluid part that is labeled as FLUID, and by iterative pressure Poisson equation calculating pressure, Poisson equation as shown in Equation (7).
Figure 862621DEST_PATH_IMAGE019
（7）
The mode that solves of Poisson equation as shown in formula (8), formula (9),
Figure 745126DEST_PATH_IMAGE020
（8）
Figure 97610DEST_PATH_IMAGE021
（9）
Wherein, adding and subtracting 1/2 is illustrated on corresponding coordinate or to negative or to 1/2 unit of positive dirction skew, the 3D texture is sampled, as shown in figure (5).
Step 9, the required pressure field according to previous step, calculate its Grad, and (any vector field can be decomposed into two other vector field sums: one is without the divergence vector field to adopt the Helmholtz-Hodge decomposition theorem, another is the gradient of scalar field, sees shown in formula (10).) the midrange speed field of fluid is projected to it get on without Divergence Field, obtain the final speed field of fluid, guarantee before and after emulation all to meet the incompressibility of fluid.
Figure 102475DEST_PATH_IMAGE022
（10）
Wherein,
Figure 540410DEST_PATH_IMAGE023
Mean the velocity field that divergence is zero;
Figure 961027DEST_PATH_IMAGE024
The velocity field that means the divergence non-zero.

Claims (5)

1. the emulation mode of the lower fluid of dynamic barrier impact, is characterized in that, the method comprising the steps of:
Step 1, the physical quantity of initialization fluid, be stored in the middle of the 3D texture;
Step 2, the midrange speed field of Semi Lagrangian scheme advection Fluid Computation;
Step 3, all dynamic barriers of voxelization, obtain 3D barrier texture and 3D boundary position texture;
Step 4, according to 3D barrier texture, the computation bound normal, be kept in the 3D normal map;
Step 5, read 3D barrier texture, records the index position of obstacles borders in texture;
Step 6, the index position according to obstacles borders in texture, extract corresponding boundary position and boundary normal and be saved in corresponding list of locations and normal list;
Step 7, according to the incompressibility of the barrier equation of motion and fluid, set up the coupling linear equation between fluid and barrier;
Step 8, CPU combines with GPU, solves the coupling linear equation, the pressure field of Fluid Computation;
Step 9, according to the gradient of pressure field, the midrange speed field of projection fluid without on Divergence Field, obtains the final speed field of fluid to it.
2. dynamic barrier according to claim 1 affects the emulation mode of lower fluid, it is characterized in that, the midrange speed field of Semi Lagrangian scheme advection Fluid Computation in described step 2, be specially: by semi-Lagrange advection step in the middle of carrying out in advance two, a forward advection and a reverse advection, then carry out two-way error compensation and aligning step, obtain more high-precision advection value.
3. dynamic barrier according to claim 1 affects the emulation mode of lower fluid, it is characterized in that all dynamic barriers of voxelization in described step 3 are specially:
Step 3.1, utilize the decrement operations that increases progressively of template buffer memory to carry out inside and outside voxelization to all dynamic barriers, and mark barrier unit is SOLID, and element of fluid is FLUID, is saved in 3D barrier texture;
Step 3.2, the barrier model is played up in each grid section one time, in geometric coloration, each triangle surface in barrier is carried out to the crossing operation of cutting into slices with grid, use bilinear interpolation to calculate the position of intersecting point coordinate, and unit, corresponding intersection point place is labeled as to BOUNDARY, mean the boundary element of barrier; In pixel coloring device, label information is rendered in the barrier texture, corresponding position of intersecting point is rendered in the boundary position texture.
4. the emulation mode of the lower fluid of dynamic barrier according to claim 1 impact, is characterized in that, the coupling linear equation of setting up according to the incompressibility of the equation of motion of barrier and fluid in described step 7 as shown in Equation (1):
Figure 523698DEST_PATH_IMAGE001
（1）
Wherein, For the transition matrix between generalized coordinate system and cartesian coordinate system, ( kThe boundary element number);
Figure 429840DEST_PATH_IMAGE004
Mass matrix for barrier;
Figure 81401DEST_PATH_IMAGE005
For the speed under generalized coordinate before barrier and fluid coupling.
5. dynamic barrier according to claim 1 affects the emulation mode of lower fluid, it is characterized in that, in described step 9, according to the gradient of pressure field, middle velocity field is carried out to projection calculating, when computing velocity divergence and pressure gradient, adopt the account form of MAC grid to be sampled to the 3D texture, on three directions of 3D texture, be offset separately 0.5 unit and sampled.
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