a fast simulation method using overlapping grids for interactions between smoke and rigid objects...

A Fast Simulation Method Using Overlapping Grids for Interactions between Smoke and Rigid Objects

A Fast Simulation Method Using Overlapping Grids for Interactions between Smoke and Rigid Objects

Yoshinori DobashiYoshinori Dobashi(Hokkaido University)(Hokkaido University)

Tsuyoshi YamamotoTsuyoshi Yamamoto(Hokkaido University)(Hokkaido University)

Tomoyuki NishitaTomoyuki Nishita(The University of Tokyo)(The University of Tokyo)

Yasuhiro MatsudaYasuhiro Matsuda(The University of Tokyo)(The University of Tokyo)

Hokkaido University http://nis-ei.eng.hokudai.ac.jp/~doba

Overview

• Introduction• Related Work• Basic Idea of Our Method• Overlapping Grids for Fluid Simulation• Resolution Determination• GPU Acceleration• Results• Conclusion



Introduction

• Visual Simulation of Natural Phenomena• Visual Simulation of Natural Phenomena

- Use of computational fluid dynamics (CFD)- Use of computational fluid dynamics (CFD)

- Fluids (smoke, fire, water, etc.)- Fluids (smoke, fire, water, etc.)

• Two types of approaches• Two types of approaches

particle basedparticle basedgrid basedgrid based


Introduction

• Grid-based approach• Grid-based approach- Simple and easy to implement- Simple and easy to implement

- Significant acceleration by GPU- Significant acceleration by GPU

terrain


Introduction

- Simple and easy to implement- Simple and easy to implement


- Inaccurate object boundary with low res. grid- Inaccurate object boundary with low res. grid

terrain

• Grid-based approach• Grid-based approach


Introduction



- Increase in computational cost with high res. grid- Increase in computational cost with high res. grid

terrain

- Inaccurate object boundary with low res. grid- Inaccurate object boundary with low res. grid

• Grid-based approach• Grid-based approach


Introduction

• Adaptive grid• Adaptive grid- Accurate object boundary- Accurate object boundary

- Increase efficiency- Increase efficiency

- Requiring restructuring of grid/mesh - Requiring restructuring of grid/mesh

terrain

- Unsuitable for GPU acceleration - Unsuitable for GPU acceleration


Introduction

• Our approach: multiple overlapping grids• Our approach: multiple overlapping grids- High res. grid for accurate object boundary- High res. grid for accurate object boundary

- No restructuring of grid- No restructuring of grid


- Suitable for GPU acceleration- Suitable for GPU acceleration

terrain


Introduction

terrain

local gridlocal grid

global gridglobal grid


Overview




Related Work• Motion of a Hot, Turbulent Gas• Motion of a Hot, Turbulent Gas [Foster97][Foster97]

- Motion of smoke due to thermal buoyancy- Use of finite difference method- Motion of smoke due to thermal buoyancy- Use of finite difference method

[Stam99][Stam99]• Stable Fluids• Stable Fluids- Fast and stable computation- Use of semi-Lagrange method- Fast and stable computation- Use of semi-Lagrange method

• Extended methods of stable fluids• Extended methods of stable fluids

[Fedkiw01][Fedkiw01] [Enright02][Enright02] [Nguyen02][Nguyen02] [Feldman03][Feldman03] [Carlson04][Carlson04]


Related Work

- Motion of smoke due to thermal buoyancy- Use of finite difference method- Motion of smoke due to thermal buoyancy- Use of finite difference method

[Stam99][Stam99]• Stable Fluids• Stable Fluids- Fast and stable computation- Use of semi-Lagrange method- Fast and stable computation- Use of semi-Lagrange method

• Extended methods of stable fluids• Extended methods of stable fluids

[Fedkiw01][Fedkiw01] [Enright02][Enright02] [Nguyen02][Nguyen02] [Feldman03][Feldman03] [Carlson04][Carlson04]

Use of single gridUse of single grid- Increase in computational cost according to number of grid points- Increase in computational cost according to number of grid points

- Inaccurate object boundary- Inaccurate object boundary

• Motion of a Hot, Turbulent Gas• Motion of a Hot, Turbulent Gas [Foster97][Foster97]


Related Work

- Use of octree data structure- Use of octree data structure

- Combination of tetrahedral mesh and regular grid- Combination of tetrahedral mesh and regular grid

• Adaptive grid/mesh• Adaptive grid/mesh

- Use of tetrahedral mesh- Use of tetrahedral mesh

[Feldman05][Feldman05] [Feldman06][Feldman06][Losasso04][Losasso04]

[Losasso04][Losasso04]

[Feldman05][Feldman05]



Related Work

- Use of octree data structure- Use of octree data structure

- Combination of tetrahedral mesh and regular grid- Combination of tetrahedral mesh and regular grid

• Adaptive grid/mesh• Adaptive grid/mesh

[Feldman05][Feldman05] [Feldman06][Feldman06][Losasso04][Losasso04]- Unsuitable for GPU acceleration- Unsuitable for GPU acceleration

- Restructuring of grid/mesh- Restructuring of grid/mesh

- Efficient computation- Efficient computation

- Accurate object boundary- Accurate object boundary

- Use of tetrahedral mesh- Use of tetrahedral mesh

[Losasso04][Losasso04]




Overview




Basic Idea of Our Method

• Use of multiple overlapping grids• Use of multiple overlapping grids

global grid

viewpoint

objectB

local grids

objectA




translate/rotate No remeshing

object

Aob

ject

A

objectBobject

A

global grid

viewpoint

local grids




objectB

obje

ctA

objectA

object

A

local grids

global grid

viewpoint

resolution is inversely proportionalto dist. from viewpoint

obje

ct A




object A

Use of stable fluid solver[Stam99] for each grid

objectB

data transferdata transfer

global gridviewpoint


Overview




Governing Equations

• Navier-Stokes Equations (NS equations)• Navier-Stokes Equations (NS equations)

u : velocity p : pressure

: density

: kinematic viscosity

f : external force

0u fuuuu

21

)(

pt


Governing Equations

object direction ofmovement

• Navier-Stokes Equations (NS equations)• Navier-Stokes Equations (NS equations)

inertial force

u : velocity p : pressure

: density

: kinematic viscosity

f : external force

0u fuuuu

21

)(

pt


Governing Equations

• Numerical solution to NS equations• Numerical solution to NS equations

)(tu

u~ fuuuuu )()()()(~ 2 ttttt

fuuuu

21

)(

pt

0u

(step1)


)(tu

u~

Governing Equations

• Numerical solution to NS equation• Numerical solution to NS equation

)(tu

u~ fuuuuu )()()()(~ 2 ttttt

fuuuu

21

)(

pt

pρ

ttt

uu ~)(

0u

Gauss-Seidel method

)( tt u

(step1)

(step2)


Simulation Using Overlapping Grids

yes

noconverged ?

)(tu

u~

u~

)( tt u

start

end

boundary transferof velocity

boundary transferof pressure

inner transferof velocity

inner transferof pressure

computationof velocity

computationof pressure

(step1) (step2)


(step1) (step2)

Simulation Using Overlapping Grids

)(tu

u~

u~

)( tt u

yes

noconverged ?

start

end

computationof velocity

computationof pressure

boundary transferof velocity

boundary transferof pressure

inner transferof velocity

inner transferof pressure


boundaryregion

Data transfer between Grids

• Case of single local grid• Case of single local grid

local grid

global grid

inner region



• Boundary transfer• Boundary transfer

local grid

global grid

(global to local)

boundaryregion

copy values



• Inner transfer• Inner transfer

local grid

global grid

(local to global)

copy values

inner region



• Case of multiple local grids• Case of multiple local grids

object

object

object

objectobject

object

object

object

objectcopy

virtual grid(highest res.)


transfertransfer transfertransfer




object

object

object

objectobject

object

object

object

objectcopy



transfertransfer transfertransfer

Large memory requirement for virtual gridLarge memory requirement for virtual grid




object

object

object

transfer

transfer

transfer

transfer

transfer

• Prioritization by the grid resolutions• Priorities used for the order of the transfer• Prioritization by the grid resolutions• Priorities used for the order of the transfer


Overview




Resolution Determination

viewpoint

• Increasing efficiency by LOD• Increasing efficiency by LOD

object

low res. grid

far

object

high res. grid

near



viewpoint


object

low res. grid

far

object

high res. grid

near

object object object

grids with different resolutionsgrids with different resolutions

simple flow


object

low res. grid


viewpoint


object

low res. grid

far

near

object object object

grids with different resolutionsgrids with different resolutions

simple flow



Re = UL

U : mean flow speedU : mean flow speedL : characteristic lengthL : characteristic length : kinematic viscosity : kinematic viscosity

characteristiclength

(longer edge)

characteristiclength

(longer edge) (mean speed)(mean speed)

• Use of Reynolds number as a measure of

complexity of flow

• Use of Reynolds number as a measure of

complexity of flow

windobject

Large Re Turbulent flow (complex flow)



• Mean flow speed / Characteristic length• Mean flow speed / Characteristic length

direction ofmovement

object

mean flow speed = speed of objectmean flow speed = speed of object

characteristic lengthcharacteristic length


Re

dh


• Condition for resolution determination• Condition for resolution determination

distance from viewpointdistance from viewpoint

grid intervalgrid interval

• grid interval distance from viewpoint∝• grid interval distance from viewpoint∝

• grid interval 1/(Reynolds number)∝• grid interval 1/(Reynolds number)∝

thresholdthreshold

Reynolds numberReynolds number


Overview




GPU Acceleration

• Use of previous method for NS solver• Use of previous method for NS solver

• Render-to-texture for data transfer• Render-to-texture for data transfer

grid ghigh grid glow3D texture

[Crane07][Crane07]


GPU Acceleration

• Boundary transfer• Boundary transfer- generate rectangles for boundary regions- generate rectangles for boundary regions

grid ghigh grid glow3D texture

rectangles


GPU Acceleration


grid ghigh grid glow

texturemapping

3D texture

rectangles


GPU Acceleration



texturemapping

3D texture

- render rectangles into 3D texture of ghigh- render rectangles into 3D texture of ghighrectangles


GPU Acceleration

• Inner transfer• Inner transfer- generate rectangles for inner regions- generate rectangles for inner regions


texturemapping

3D texture

- render rectangles into 3D texture of glow- render rectangles into 3D texture of glow

rectanglesRealizing fast data transfers just by

drawing rectangles

Realizing fast data transfers just by

drawing rectangles


Overview




Experimental Results

• 2D simulation on CPU• 2D simulation on CPU

global only(150x300)


overlapping(100x100+150x300)



• 2D simulation on CPU• 2D simulation on CPU

0.5s 0.18s0.07s



overlapping(100x100+150x300)

computation times/time-step

2.8 times faster computation

(CPU： Pentium4 3.8 GHz)



reference our method

• Experiment using 3D simulation on CPU• Experiment using 3D simulation on CPU


Practical Examples

• Real-time 2D simulation on GPU• Real-time 2D simulation on GPU

- global grid: 5122- global grid: 5122

- local grid: 1282

(for each letter)- local grid: 1282

(for each letter)

- computation time: 28 fps on GeForce8800 ultra



Practical Examples

• Real-time 3D simulation on GPU• Real-time 3D simulation on GPU

- global grid: 41x59x25- global grid: 41x59x25

- local grid: 1283

(for a fighter)- local grid: 1283

(for a fighter)



(0.14 fps on CPU)(0.14 fps on CPU)

(71 times faster !)


Practical Examples

• Dynamic smoke from fighter planes• Dynamic smoke from fighter planes

fighterfighter missilemissile


Conclusion

• Efficient simulation using overlapping grids• Efficient simulation using overlapping grids

- Single global grid + multiple local grids around moving objects - Single global grid + multiple local grids around moving objects

- Rotating/translating local grids move according to motion of objects- Rotating/translating local grids move according to motion of objects

- Adaptive resolution determination of local grids- Adaptive resolution determination of local grids

- Significant speedup achieved by GPU- Significant speedup achieved by GPU

a fast simulation method using overlapping grids for interactions between smoke and rigid objects...

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