Flame Animation

Team : Fire!20061237 Lee, Ho-Jin

20071229 Kim, Young Soo

Objective

• Modeling the flame physically and realistically

• Rendering of the result of simulated flame

Physical Modeling Function

• INPUT : Temperature, Pressure, Den-sity, Velocity, Material in specific time

• OUTPUT : RGB Color Value

• Physically simulate the flame and make data for rendering

Fluid Simulation

• Get variables of each cell in next time step from data of given time

Picture from [S-tam99]

Navier-Stokes Equation

• Equation to describe the state of vis-cous fluid

• Navier-Stokes Eq. for incompressible fluids was used for simulation

2 2 2

2 2 2 x

u u u u p u u uu v w g

t x y z dx x y z

Velocity

Fluid Modeling

• Amount of moved fluid depends on density and velocity

Fluid Modeling

• Derivative of density is proportional to the amount of transferred gas

• From equation of ideal gas state

P T

1 1( ) ( )ii i i iu u

t

Fluid Modeling

• Because internal energy of gas is time derivative of Temperature is

3

2U nRT

1 1 1 1( ) ( ) ( ) ( )ii i i i i i i i

Tu T T u T T

t

Material Modeling

• Like the thermal flow, oxygen and fuel flow is

,, 1 , , , 1( ) ( )oxygen i

oxygen i oxygen i oxygen i oxygen i

mm m u m m u

t

,, 1 , , , 1( ) ( )fuel i

fuel i fuel i fuel i fuel i

mm m u m m u

t

Material Modeling

• According to Chemical Kinetics and Arrhenius’s Equation, the amount of burned fuel is

• Then energy conservation law gives

, , /,

oxygen i fuel i Tburned i

i i

m mm e

,i

burned i

Tm

t

Get RGB Value from Vari-ables

• Emitted energy proportional to the amount of burned fuel

• RGB Values depends on temperature– In the basic case, it changes form red in

low temperature to yellow in high tem-perature

Simulation Scheme

Calculate Velocity•From Navier-Stokes Equa-tion

Calculate Variables•Computational Fluid Dynam-ics

• Include pressure, density and temperature

Compute Fuel’s Burn-ing Effect•Temperature Change•Emitting Energy

Get Light form Cell•Get RGB Value•Spectrum depends on mate-rial property and tempera-ture

• Intensity depends on emit-ted energy

Volume Rendering

• 각각의 Cell 을 Volume Rendering 을 사용

• Volume 감 있는 Fire Animation 을 표현

Volume Rendering

• 반투명한 GLUT 의 Cube 를 이용해 그리드의 각 Cell 들의 색상 랜더링

• Alpha Blending 시에는 Z-Buffering에만 의존할 수 없으므로 시점에 따라 뒤에서부터 그려주게 코드 작성

Example [RGB Cube]• Different Alpha Channel Value (A= 120, 60,

30, 5)

• Different Cell Grid Size (N = 10, 20, 50)

Demo

GRIDSIZE = 10

GRIDSIZE = 10

GRIDSIZE = 10

Conclusion

• Successfully modeled flame physi-cally– But couldn’t find realistic and stable so-

lution– Navier-Stokes Equation Solver should be

more stable

• Rendered explosion

Future works

• Develop more stable CFD Solver

• Implement Solver for GPGPU

• Volume Rendering using Ray Casting with GPU

Reference

• Wikipedia : Navier-Stokes Equations (http://en.wikipedia.org/wiki/Navier_Stokes, 2009.06.22 현재 )

• Jos Stam, "Stable Fluids", SIGGRAPH 1999, 121-128, 1999

• Jos Stam, "Real-Time Fluid Dynamics for Games", Game Developer Conference 2003

• Wikipedia : Arrhenius Equation (http://en.wikipedi-a.org/wiki/Arrhenius_equation, 2006.06.22 현재 )

• Keenan Crane et al, Real-Time Simulation and Ren-dering of 3D Fluids, GPU Gems 3, 633-675, Addison-Wesley Professional, 2007

Thank You