Physical Based Modeling Physical Based Modeling and Animation of Fire and and Animation of Fire and

Water SurfaceWater Surface

Jun Ni, Ph.D. M.E.Associate Research Scientist, Research Services

Adjunct Assistant ProfessorDepartment of Computer Science

Department of Mechanical Engineering

Presented at Prof. Joe KeaRney’s animation lecture

Dr. Ronald Fediw

Department of Computer Science, Stanford University

Conference proceeding at ACM SIGGRAPH 2002

Animation of FireAnimation of FireOutlineOutline

IntroductionIntroduction Physical Based ModelPhysical Based Model Level-set ImplementationLevel-set Implementation Rendering of FireRendering of Fire Animation ResultsAnimation Results

IntroductionIntroduction Modeling of natural phenomena such as fire Modeling of natural phenomena such as fire

and water remains a challenging problem in and water remains a challenging problem in computer graphicscomputer graphics

Complications of the modelingComplications of the modeling fluid motion with un-stability, transient, non-linear, fluid motion with un-stability, transient, non-linear,

multi-phases, and multi-component, combustion multi-phases, and multi-component, combustion (chemical reactions), different physical scales, fluid (chemical reactions), different physical scales, fluid compression, explosions and wavecompression, explosions and wave

For example, fluid reaction systemFor example, fluid reaction system Combustion processes can be classified into two Combustion processes can be classified into two

distinct types of phenomenadistinct types of phenomena DetonationsDetonations DeflagrationsDeflagrations

Introduction to physical Introduction to physical phenomenaphenomena

DeflagrationsDeflagrations : low speed events with : low speed events with chemical reactions converting fuel into hot chemical reactions converting fuel into hot gaseous products, such as fire and flame. gaseous products, such as fire and flame. They can be modeled as an incompressible They can be modeled as an incompressible and inviscid (less viscous) flowand inviscid (less viscous) flow

Detonations: high speed events with Detonations: high speed events with chemical reactions converting fuel into hot chemical reactions converting fuel into hot gaseous productions with very short period gaseous productions with very short period of time, such as explosions (shock-wave of time, such as explosions (shock-wave and compressible effects are important)and compressible effects are important)

Introduction to ModelingIntroduction to Modeling How to model?How to model?

Introduce Introduce a dynamic implicit surfacea dynamic implicit surface to track to track the reaction zone where the gaseous fuel is the reaction zone where the gaseous fuel is converted into the hot gaseous productsconverted into the hot gaseous products

The gaseous fuel and hot gaseous zones are The gaseous fuel and hot gaseous zones are modeled separately by using independent modeled separately by using independent sets of incompressible flow equations.sets of incompressible flow equations.

Coupling the separate equations by Coupling the separate equations by considering the mass and momentum considering the mass and momentum balances along the reaction interface (the balances along the reaction interface (the surface)surface)

Introduction to ModelingIntroduction to Modeling How to model?How to model?

Rendering the fire as a participating Rendering the fire as a participating medium with black body radiation using medium with black body radiation using stochastic ray marching algorithmstochastic ray marching algorithm

Chromatic adaptation of observer to get Chromatic adaptation of observer to get the reaction colors of the firethe reaction colors of the fire

Physical Based ModelPhysical Based Model Three distinct visual phenomena:Three distinct visual phenomena:

Blue or bluish-green coreBlue or bluish-green core: emission lines from : emission lines from intermediate chemical species, such as carbon intermediate chemical species, such as carbon radical generated during reaction. It is located radical generated during reaction. It is located adjacent to the implicit surface imposed. this color adjacent to the implicit surface imposed. this color can be used to track the movement of the surfacecan be used to track the movement of the surface

Yellowish-orange colorYellowish-orange color: blackbody radiation : blackbody radiation emitted by the hot gaseous products (carbon soot)emitted by the hot gaseous products (carbon soot)

Fire soot or smoke coreFire soot or smoke core: temperature cools to the : temperature cools to the point where the blackbody radiation is no longer point where the blackbody radiation is no longer visiblevisible

solid fuel

gas fuel

blue core

ignition

T max

Temperature

time

gas products

gas to solid phase change

Soot emit blackbody radiation that illuminates smoke

Blue core

Hot gaseous products

Physical Based ModelPhysical Based Model Blue or bluish-green coreBlue or bluish-green core::

surface area of the blue core is determined surface area of the blue core is determined byby

vfAf = SAs

Vf is the speed of fuel injected, Af is the cross section area of cylindrical injection

S

vf

AsImplicit surface

Un-reacted gaseous fuel

Reacted gaseous fuel

Af

Blue reaction zone cores with increased speed S (left); with decreased speed S (right)

S is large and core is small

S is small and core is large

Physical Based ModelPhysical Based Model Premixed flame and diffusion flamePremixed flame and diffusion flame

fuel and oxidizer are premixed and gas is fuel and oxidizer are premixed and gas is ready for combustionready for combustion

non-premixed (diffusion)non-premixed (diffusion)

fuel fuel

diffusion flame

premixed flame

Location of blue reaction zone

oxidizer

Physical Based ModelPhysical Based Model Hot Gaseous ProductsHot Gaseous Products

Expansion parameter Expansion parameter ff//hh

h=0.2 0.1 0.02

f=1.0

Physical Based ModelPhysical Based Model Mass and momentum conservation Mass and momentum conservation

require require h(Vh-D)=f(Vf-D)

h (Vh-D)2 +ph = rf(Vf-D)2+pf

Vf and Vh are the normal velocities of fuel and hot gaseousD =Vf-S speed of implicit surface direction

Physical Based ModelPhysical Based Model Solid fuelSolid fuel

Use boundary as Use boundary as reaction front reaction front

Vf=Vs+(s /f-1)S

s and Vs are the density and the normal velocity of solid fuel

Solid fuel

ImplementationImplementation Discretization of physical domain into Discretization of physical domain into

NN33 voxels (grids) with uniform spacing voxels (grids) with uniform spacing Computational variables implicit Computational variables implicit

surface, temperature, density, and surface, temperature, density, and pressure, pressure, i,j,ki,j,k, T, Ti,j,ki,j,k, , i,j,ki,j,k, and p, and pi,j,ki,j,k

Track reaction zone using level-set Track reaction zone using level-set methods, methods, =+,-, and 0, representing =+,-, and 0, representing space with fuel, without fuel, and space with fuel, without fuel, and reaction zonereaction zone

Implicit surface moves with velocity Implicit surface moves with velocity w=uw=uff+s+snn, so the surface can be , so the surface can be governed bygoverned by

t= - w

ImplementationImplementation Incompressible flow for gaseous Incompressible flow for gaseous

fuel and hot gaseous product zonefuel and hot gaseous product zone

ut= - (u ) u - p/ +(T-Tair)z

p/( ) =

u=0

u*/ t

ImplementationImplementation Temperature and densityTemperature and density

T=TT=Tignitionignition for blue zone for blue zone Linear interpolation between TLinear interpolation between Tignitionignition

and Tand Tmax max for hot gaseous product zonefor hot gaseous product zone Energy conservationEnergy conservation

T = - (u ) T – Ct ( )T-Tair

Tmax-Tair

4

Rendering of FireRendering of Fire Fire: participating mediumFire: participating medium

Light energyLight energy Bright enough to our eyes adapt its colorBright enough to our eyes adapt its color Chromatic adaptationChromatic adaptation ApproachesApproaches

Simulating the scattering of the light within a Simulating the scattering of the light within a fire mediumfire medium

Properly integrating the spectral distribution Properly integrating the spectral distribution of the power in the fire and account for of the power in the fire and account for chromatic adaptationchromatic adaptation

Rendering of FireRendering of Fire Light Scattering in a fire mediumLight Scattering in a fire medium

Fire is a blackbody radiator and a Fire is a blackbody radiator and a participating mediumparticipating medium

Properties of participating are described byProperties of participating are described by Scattering and its coefficientScattering and its coefficient Absorption and its coefficientAbsorption and its coefficient Extinction coefficientExtinction coefficient EmissionEmission

These coefficients specify the amount of These coefficients specify the amount of scattering, absorption and extinction per scattering, absorption and extinction per unit-distance for a beam of light moving unit-distance for a beam of light moving through the mediumthrough the medium

Rendering of FireRendering of Fire Phase function p(g, Phase function p(g, ) is introduced to ) is introduced to

address the distribution of scatter address the distribution of scatter light, where g(-1,0) (for backward light, where g(-1,0) (for backward scattering anisotropic medium) g(0) scattering anisotropic medium) g(0) (isotropic medium), and g(0,1) (for (isotropic medium), and g(0,1) (for forward scattering anisotropic forward scattering anisotropic medium)medium)

Light transport in participating Light transport in participating medium is described by an integro-medium is described by an integro-differential equationdifferential equation L(x,w)=f(coefficients, L, Le, )

Spectral radianceIncoming direction angle of scattering light

Emitted radiance

Rendering of FireRendering of Fire Reproducing the color of fireReproducing the color of fire

Full spectral distribution --- using Full spectral distribution --- using Planck’s formula for spectral radiance Planck’s formula for spectral radiance in ray machiningin ray machining

The spectrum can be converted to The spectrum can be converted to RGB before being displaying on a RGB before being displaying on a monitormonitor

Need to computer the chromatic Need to computer the chromatic adaptation for fire --- hereby using a adaptation for fire --- hereby using a transformation Fairchild 1998)transformation Fairchild 1998)

Rendering of FireRendering of Fire Reproducing the color of fireReproducing the color of fire

Assumption: eye is adapted to the Assumption: eye is adapted to the color of the spectrum for maximum color of the spectrum for maximum temperature presented in the firetemperature presented in the fire

Map the spectrum of this white point Map the spectrum of this white point to LMS cone responsivities (Lto LMS cone responsivities (Lww, M, Mww, , SSww) (Fairchild ‘s book “color ) (Fairchild ‘s book “color appearance model”, 1998)appearance model”, 1998)(Xa, Ya, Za) (Xr, Yr, Zr)

Adapted XYZ tristimulus valuesraw XYZ tristimulus values

Animation ResultAnimation Result Domain: 8 meters long with 160 Domain: 8 meters long with 160

grids (increment h=0.05m)grids (increment h=0.05m) VVff=30m/s A=30m/s Aff=0.4m=0.4m S=0.1m/sS=0.1m/s ff=1=1 hh=0.01=0.01 Ct=3000K/sCt=3000K/s =0.15 m/(Ks2)=0.15 m/(Ks2)

A metal ball passing through and interacts with a gas flame

A flammable ball passes through a gas flame and catches on fire

It is time to see several animations!

Animation of WaterAnimation of WaterOutlineOutline

IntroductionIntroduction Physical Based Simulation ModelPhysical Based Simulation Model Particle -Level-set MethodParticle -Level-set Method Rendering of WaterRendering of Water Animation ResultsAnimation Results

IntroductionIntroduction Photorealistic simulation of water Photorealistic simulation of water

surfacesurface Treatment of the surface separating Treatment of the surface separating

the water from airthe water from air Two-phase problemTwo-phase problem Providing visual impression of water Providing visual impression of water

with surfacewith surface Key point is to model the surfaceKey point is to model the surface Approach: particle level-set methodApproach: particle level-set method

IntroductionIntroduction Particle level-set methodParticle level-set method

Hybrid surface tracking method using Hybrid surface tracking method using mass-less marker particles combined mass-less marker particles combined with a dynamic implicit surfacewith a dynamic implicit surface

An implicit surface imposed to An implicit surface imposed to representing water surface during representing water surface during computation.computation.

IntroductionIntroduction Particle level-set methodParticle level-set method

Velocity extrapolation procedure across Velocity extrapolation procedure across the water surface into the region occupied the water surface into the region occupied by the air.by the air.

Control the behavior of water surfaceControl the behavior of water surface Add dampening and/or churning effectsAdd dampening and/or churning effects

IntroductionIntroduction Rendering of waterRendering of water

Relatively easy, since it optical Relatively easy, since it optical properties are well understood and properties are well understood and can be well described.can be well described.

Surface tension caused illuminationSurface tension caused illumination There are several algorithmsThere are several algorithms

Path tracingPath tracing Bidirectional path tracingBidirectional path tracing Metropilis light transportMetropilis light transport Photon mappingPhoton mapping

Simulation MethodsSimulation Methods Liquid volume model (previous Liquid volume model (previous

model)model) Implicit function, Implicit function, (<0 water, >0 (<0 water, >0

air, =0 surface) (Foster and air, =0 surface) (Foster and Fedkiw, 2001)Fedkiw, 2001)t + u = 0

Particle motion transport equation

Using previous model

Using modified model

Simulation MethodsSimulation Methods Particle Level-set model (modified Particle Level-set model (modified

or particle enhanced level-set or particle enhanced level-set model)model)

Impose two sets (positive and Impose two sets (positive and negative particles) on both sides of negative particles) on both sides of fluid regions separated by the fluid regions separated by the implicit surfaceimplicit surface

Simulation MethodsSimulation Methods Radius of particle changes Radius of particle changes

dynamics throughout the dynamics throughout the simulation and is based on level-set simulation and is based on level-set function function ..

rp ={rmax if sp(xp)>rmax

rmin if sp(xp)<rmin

sp(xp) rmin<sp(xp)<rmax

Sign function (1 for positive particle and -1 for negative particle)

Simulation MethodsSimulation Methods Extrapolation method for air Extrapolation method for air

motionmotion

uutt = -N = -N u

Unit velocity perpendicular to the implicit surface

N

u is velocity in x component

Simulation MethodsSimulation Methods equation for fluid motion (N-S)equation for fluid motion (N-S)

uutt = -u = -u u+ ( u) - p +g1

Simulation MethodsSimulation Methods Variables are p , Variables are p , , , and u and u Current surface velocity is Current surface velocity is

smoothly extrapolated across the smoothly extrapolated across the surface into the air regionsurface into the air region

Water surface and maker particles Water surface and maker particles are integrated forward in timeare integrated forward in time

RenderingRendering Physically based Monte Cargo ray Physically based Monte Cargo ray

tracer capable of handling all types of tracer capable of handling all types of illumination using photon maps and illumination using photon maps and irradiance caching (Jensen 2001)irradiance caching (Jensen 2001)

Level-set function have two Level-set function have two advantagesadvantages Intersecting ray with surface is must Intersecting ray with surface is must

efficient, especially for isosurfaceefficient, especially for isosurface Provide motion of blur in standard Provide motion of blur in standard

distribution ray tracing frameworkdistribution ray tracing framework

Two animation resultsTwo animation results Pouring water into a glassPouring water into a glass Breaking waveBreaking wave

Theoretical wave solution (Radovitzky Theoretical wave solution (Radovitzky and Oritz, 1998) to obtain u(x,y), v(x,y) and Oritz, 1998) to obtain u(x,y), v(x,y) and and (x,y) (surface height)(x,y) (surface height)

Water being poured into a clear, cylindrical glass (55x55x120 grid cell)

Breaking wave on a submerged shell (540x75x120 grid cell)