Physically based animatio n of sandstorm

1. Physically based animation of sandstorm Shiguang Liu, Zhangye Wang, Zheng Gong, Lei Huang, and QunshengPeng (presented by Kam, Hyeong Ryeol)

2. Contents • Abstract • Introduction • Related Work • Modeling of the Sandstorm • Rendering of Sandstorm Scene • Results and Discussion • Conclusion and Future Works

3. Abstract • Physically based method for modeling and animating sandstorm • Stable incompressible multiple fluid model • Based on Reynold-average Navier-Stokes equations. • The sand and dust particle flow is computed taking interaction among the wind, sand, and dust particles into account. • Multi-Fluid Solver is designed and implemented on GPU. • Various illumination effects of sandstorm scenes can be simulated by spectral sampling scattering calculation.

4. Introduction • There were little attention to this area • We propose a fast, physically based, and easily implemented method for modeling and animating realistic sandstorm scenes. • Sandstorm carries huge amount of sand and dust • The wind is caused by convection currents created by intense heating of the ground. • Air is unstable when heated • This causes the mixture of higher winds in the troposphere with winds in the lower atmosphere, incurring strong surface winds.

5. Introduction • We propose a physically based method for modeling and animating sandstorm • 1. We establish the unstable wind field of sandstorm based on RANS. • The motion of sand and dust particle is regarded as the continuous flows (expressed by the non-viscosity fluid model) • 2. We propose a GPU-based Multi-Fluid Solver for dynamic sandstorm scene. • 3. Spectral sampling of the scattering light. • 4. According to the statistical distribution of the size of sand and dust particles, fantastic illumination effects of sandstorm in different areas and at different stages are rendered.

6. Related Work • Studying the motion of sandstorm by experimental data or numerical analysis method • Joseph et al. studied the relationship between the weather conditions and velocity of sandstorm. • Aiming at calculating the movement of sandstorm • Too complicated to be visualized • For simulation of fluid-like natural phenomena, most works adopt fluid models. • Volume of fluid • Conserving mass, tracking and locating the free surface • Moving particle semi-implicit • Incompressible fluid / gridless particle method

7. Related Work • Chemical reaction may exist. • ex) combustion • Two-Fluid model • Two-Fluid Lattice Boltzmann model • Miscible binary mixtures • Volcanic clouds • Gas-solid flow / Conveyed by the velocity field • Interaction during explosion / Drag force • Sand particle are conveyed by the velocity field AND the interaction between sand particles and the air flow.

8. Related Work • Realistic simulation of sandstorm • A method of modeling granular materials(sand, grains) • Helps to simulate phenomena like splashing or avalanches • Modeling and rendering realistic desert scene include sand dunes and wind ripples • Bump-mapping using Level of Detail.

9. Modeling of the Sandstorm • We consider sandstorm as a multi-fluid composed of wind, sand, and small dust particles flows. • Wind field • Sand and dust particle flow model • Interaction among wind, sand, and dust particle flow • Multi-fluid solver on GPU

10. Modeling of the Sandstorm- Wind Field • Wind Field • Stable near-surface air flow : Navier-Stokes equations. • Unstable air flow : Reynold-average Navier-Stokes • Sandstorm - (considering the effects of the atmospheric turbulence)

11. Modeling of the Sandstorm- Wind Field • The velocity distribution around a sand particle • Reynold shear stress is • (a) not considered • (b) considered

12. Modeling of the Sandstorm- Sand and Dust Particle Flow Model • Since a sandstorm consists of a huge number of sands and dust particles, so tracing each particle is not feasible. • Particles’ movements obey statistical distribution like fluid so we can approximate the motion of sand and dust particle as non-viscosity, incompressible fluid like below:

13. Modeling of the Sandstorm- Sand and Dust Particle Flow Model • The force of a single particle in air flow • Suppose • the sand and dust particles : spherical • The particles move in XOY plane • This force consists of • The valid gravity of sand particle • The entrainment force by air flow : most important • produced by the velocity difference between the air flow and the sand particle flow

14. Modeling of the Sandstorm- Sand and Dust Particle Flow Model • The force of a single particle in air flow • the valid gravity of particle • the entrainment force • the coefficient of resistance Buoyancy of the sand particle in the air flow

15. Modeling of the Sandstorm- Interaction Among Wind, Sand, and Dust Particle Flow • The sand and dust particles are entrained by the wind. • The velocity of the wind will be affected by the counterforce of the sand and dust particle flow • Sandstorm’s external force is the interaction force betweensand particle flow and air flow (caused by the velocity difference between them)

16. Modeling of the Sandstorm- Interaction Among Wind, Sand, and Dust Particle Flow • The wind field, sand, and dust particle flows can be regarded as continuous fluid. • Interaction among these can be modeled as that between wind field and a group of particles • We account the sand and dust particles in a unit volume as a whole • The counterforce to the wind field by the sand and dust particle flow is • Equivalent to adding a body force to the wind field model

17. Modeling of the Sandstorm- Interaction Among Wind, Sand, and Dust Particle Flow • The diameter distribution of sand and dust particles in sandstorms L : low / M : moderate / S : High visibilities

18. Modeling of the Sandstorm- Interaction Among Wind, Sand, and Dust Particle Flow • Due to the diameter of sand and dust particle is very small, the interaction force between them can be ignored. • The interaction force between sand particles in a unit volume and the air flow :

19. Modeling of the Sandstorm- Multi-Fluid Solver on GPU • Our model describes a multiple fluid system • Air flow • Sand and dust particle flows. • We solve the multiple Navier-Stokes equations in parallel in one rendering pass by combining multiple field data texture into one texture. • It reduces the calculating time • Flat 3D texture technique • It’s easy to read and store velocity data

20. Modeling of the Sandstorm- Multi-Fluid Solver on GPU • The calculation flow • 1. Initialize the air flow and sand particle flow • 2. Set the initial condition and boundary condition • 3. Solve the NS equations on GPU by the Semi-Lagrange methods. • The size of our flat 3D texture is several times as large as that of the previous method, but it doesn’t affect the calculation efficiency for the linear calculation function of GPU

21. Modeling of the Sandstorm- Multi-Fluid Solver on GPU • Flow chart of Multi-Fluid Solver • With this, we can solve multiple NS in parallel in one rendering pass.

22. Rendering of Sandstorm Scene • To show realistically, we must consider the interaction of various types of components of sandstorm with light. • Scattering / Absorption effect of particles • Our rendering model of sandstorm scene is based on multiple Mie scattering theory • We adopt pre-computation technique to accelerate the rendering rate.

23. Rendering of Sandstorm Scene- Mie Scattering Model for Natural Light • Theory for scattering of spherical particles • For particle sizes larger than a wavelength • Produces a pattern like an antenna lobe, with a sharper and more intense forward lobe for larger particles. • Not strongly wavelength dependent and produces the almost white glare

25. Rendering of Sandstorm Scene- Calculation of Scattering in Sandstorm • The shape of the majority of sand and dust particles is spherical • The effect of scattering can be determined by measuring the intensity Isca of a light ray after traveling l distance. • If I0 is the intensity of the light source, • the ratio is • According to Bougure Law

26. Rendering of Sandstorm Scene- Calculation of Scattering in Sandstorm • Considering the distribution of sand particles in sandstorm, we define the scattering coefficient of sand particles in a unit volume as • Since the computation of the Mie scattering is very complicated including calculation of scattering section and scattering coefficient, we use a new method to pre-compute these terms of sand particles

27. Rendering of Sandstorm Scene- Rendering of Sandstorm Scene • Multiple scattering effect of sands • discrete the space filled with sandstorm into voxels • For each voxelPi,j, its incident radiance from direction w includes the direct light from the light source in direction w and multiple scattered light from other voxels. • Multiple scattering model is :

28. Rendering of Sandstorm Scene- Calculation of Scattering in Sandstorm • In-scattering from the six neighboring voxels are sampled, so • For scattering of sand particles is almost isotropic, we consider the phase function as constant

29. Rendering of Sandstorm Scene- Calculation of Scattering in Sandstorm • Rendering method : a two-pass algorithm • We pre-compute the shading of sandstorm scene according to the position of each voxeland the incident direction of light source in the first pass. ▼ • We use the shading result • To render the scene under fixed viewpoint in the second pass

30. Results and Discussion • With the increase of the density of sand and dust particles, the scattering color is changing gradually from light yellow to yellow, then to red, and the visibility decreases correspondingly • The color change is mainly caused by the change of density distribution of sand particles. • Our method is based on physical theory •  The appearance of sandstorm and scattering effects of the road lamp looks realistic.

31. Results and Discussion • Figure 8 • (a) rendering result • (b) the real photo

32. Results and Discussion • Figure 9 • (a) rendering result • (b) the real photo

33. Results and Discussion • Figure 10 • (a) high visibility • (b) moderate visibility • (c) low visibility

34. Results and Discussion • Figure 11 • Near the viewpoint

35. Results and Discussion • Figure 12 • Sandstorm scenes with moderate visibility

36. Conclusion and Future Works • Our method adopts multi-phase fluid models to simulate the motion of air, sand, and dust particles in the sandstorm. • The wind field is established by RANS equations • The sand and dust particle flow is built with the non-viscosity fluid model taking the statistical distribution of particles of varied size into account. • We design a Multi-Fluid Solver and implement it on GPU • By spectral sampling of the light scattering, the peculiar illumination effect of dynamic sandstorm scenes is revealed.

37. Conclusion and Future Works • Contributions • 1. It is the first time to simulate dynamic sandstorm scene based on physical principles. • 2. We adopt multiple fluid model on GPU to deal with the motion and the complex interaction fast. • 3. System is easy to implement. Users can generate various realistic sandstorm scenes with different visibility at different stages.

38. Conclusion and Future Works • Future Work • This model can be extended to simulate other phenomena of multiple gas-solid mixtures • But, oil-water-like phenomena is our next goal • Dynamic sandstorm model is still far from perfect • It’s like fog when it is close to the view point • Euler-based method combining with particle system suggests a potential way for overcoming this limitation. • We will simulate other natural disastrous phenomena • Such as debris flow, avalanche, etc

39. The End • Any Questions??