Fluid Simulation for Computer Graphics 77P 硕士论文

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【核心代码】

Contents
1 Introduction 10
2 Related work 11
2.1 Advection......................................................................................................11
2.2 Surface Tracking.............................................................................................12
2.3 Pressure Projection.........................................................................................12
2.4 Fluid-Solid Interaction.....................................................................................12
2.5 Other Approaches...........................................................................................12
3 Fluid Simulation 13
3.1 Simulation Viewpoints.....................................................................................13
3.2 Fluid Equations...............................................................................................14
 3.2.1 Symbols................................................................................................14
 3.2.2 Momentum equation...............................................................................14
 3.2.3 Incompressibility condition......................................................................16
3.3 Viscosity........................................................................................................17
3.4 Numerical Simulation......................................................................................18
 3.4.1 Fluid Algorithm.......................................................................................18
 3.4.2 MAC Grid...............................................................................................18
3.5 Advection......................................................................................................20
 3.5.1 Semi-Lagrangian Advection.....................................................................20
 3.5.2 Interpolation..........................................................................................20
 3.5.3 MacCormack Method...............................................................................21
3.6 Pressure Solve................................................................................................22
 3.6.1 Projection and Linear System Solve..........................................................22
3.7 Smoke...........................................................................................................25
 3.7.1 Smoke sources.......................................................................................25
 3.7.2 Heat and smoke diffusion........................................................................25
 3.7.3 Vorticity confinement..............................................................................26
 3.7.4 Divergence Control.................................................................................26
3.8 Surface tracking.............................................................................................28
 3.8.1 Tracker particles.....................................................................................28
 3.8.2 Level Set Method....................................................................................29
 3.8.3 Particle Level Set....................................................................................31
3.9 Accurate Pressure Solves.................................................................................33
 3.9.1 Ghost fluid method.................................................................................33
 3.9.2 Surface tension......................................................................................35
3.10 Coupling Fluids and Solids................................................................................37
 3.10.1 One way coupling.................................................................................37
 3.10.2 Weak Coupling.....................................................................................37
3.11 Terrain...........................................................................................................38
3.12 Implementation..............................................................................................40
 3.12.1 Classes................................................................................................40
 3.12.2 Rendering options.................................................................................41
 3.12.3 Results................................................................................................44
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4 Work focus 55
4.1 Hybrid grid structure........................................................................................55
 4.1.1 Original method......................................................................................55
 4.1.2 Discretization..........................................................................................55
 4.1.3 Remeshing.............................................................................................57
 4.2 Our method: A more general hybrid grid structure...............................................58
 4.2.1 Details...................................................................................................58
 4.2.2 Timings..................................................................................................60
4.3 Multi-Threaded Advection..................................................................................60
 4.3.1 Timings..................................................................................................61
4.4 Hybrid Grid Structure and Multi-Threaded Advection combined..............................63
4.5 Result comparison............................................................................................64
 4.5.1 Surface tension.......................................................................................65
5 Conclusions and Future work 70
5.1 Conclusions.....................................................................................................70
5.2 Future Work....................................................................................................71
 5.2.1 Simulation quality...................................................................................71
 5.2.2 Simulation speed.....................................................................................72
Appendix 73
References 74