P HYSICALLY BASED ANIMATION OF SANDSTORM Shiguang Liu, Zhangye Wang, Zheng Gong, Lei Huang, and Qunsheng Peng (presented by Kam, Hyeong Ryeol)

C ONTENTS Abstract Introduction Related Work Modeling of the Sandstorm Rendering of Sandstorm Scene Results and Discussion Conclusion and Future Works

A BSTRACT 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.

I NTRODUCTION 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.

I NTRODUCTION 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.

R ELATED W ORK 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

R ELATED W ORK 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.

R ELATED W ORK 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.

M ODELING OF THE S ANDSTORM 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

M ODELING OF THE S ANDSTORM - W IND F IELD 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)

M ODELING OF THE S ANDSTORM - W IND F IELD The velocity distribution around a sand particle Reynold shear stress is (a) not considered (b) considered

M ODELING OF THE S ANDSTORM - S AND AND D UST P ARTICLE F LOW M ODEL 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:

M ODELING OF THE S ANDSTORM - S AND AND D UST P ARTICLE F LOW M ODEL 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

M ODELING OF THE S ANDSTORM - S AND AND D UST P ARTICLE F LOW M ODEL 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

M ODELING OF THE S ANDSTORM - I NTERACTION A MONG W IND, S AND, AND D UST P ARTICLE F LOW 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 between sand particle flow and air flow (caused by the velocity difference between them)

M ODELING OF THE S ANDSTORM - I NTERACTION A MONG W IND, S AND, AND D UST P ARTICLE F LOW 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

M ODELING OF THE S ANDSTORM - I NTERACTION A MONG W IND, S AND, AND D UST P ARTICLE F LOW The diameter distribution of sand and dust particles in sandstorms L : low / M : moderate / S : High visibilities

M ODELING OF THE S ANDSTORM - I NTERACTION A MONG W IND, S AND, AND D UST P ARTICLE F LOW 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 :

M ODELING OF THE S ANDSTORM - M ULTI -F LUID S OLVER 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

M ODELING OF THE S ANDSTORM - M ULTI -F LUID S OLVER 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

M ODELING OF THE S ANDSTORM - M ULTI -F LUID S OLVER ON GPU Flow chart of Multi-Fluid Solver With this, we can solve multiple NS in parallel in one rendering pass.

R ENDERING OF S ANDSTORM S CENE 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.

R ENDERING OF S ANDSTORM S CENE - M IE S CATTERING M ODEL FOR N ATURAL L IGHT 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

R ENDERING OF S ANDSTORM S CENE - C ALCULATION OF S CATTERING IN S ANDSTORM The shape of the majority of sand and dust particles is spherical The effect of scattering can be determined by measuring the intensity I sca of a light ray after traveling l distance. If I 0 is the intensity of the light source, the ratio is According to Bougure Law

R ENDERING OF S ANDSTORM S CENE - C ALCULATION OF S CATTERING IN S ANDSTORM 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

R ENDERING OF S ANDSTORM S CENE - R ENDERING OF S ANDSTORM S CENE Multiple scattering effect of sands discrete the space filled with sandstorm into voxels For each voxel P i,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 :

R ENDERING OF S ANDSTORM S CENE - C ALCULATION OF S CATTERING IN S ANDSTORM 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

R ENDERING OF S ANDSTORM S CENE - C ALCULATION OF S CATTERING IN S ANDSTORM Rendering method : a two-pass algorithm We pre-compute the shading of sandstorm scene according to the position of each voxel and 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

R ESULTS AND D ISCUSSION 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.

R ESULTS AND D ISCUSSION Figure 8 (a) rendering result (b) the real photo

R ESULTS AND D ISCUSSION Figure 9 (a) rendering result (b) the real photo

R ESULTS AND D ISCUSSION Figure 10 (a) high visibility (b) moderate visibility (c) low visibility

R ESULTS AND D ISCUSSION Figure 11 Near the viewpoint

R ESULTS AND D ISCUSSION Figure 12 Sandstorm scenes with moderate visibility

C ONCLUSION AND F UTURE W ORKS 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.

C ONCLUSION AND F UTURE W ORKS 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.

C ONCLUSION AND F UTURE W ORKS 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

T HE E ND Any Questions??