1. Flame Animation Team : Fire! 20061237 Lee, Ho-Jin 20071229 Kim, Young Soo

2. Objective Modeling the flame physically and realistically Rendering of the result of simulated flame

3. Physical Modeling Function INPUT : Temperature, Pressure, Density, Velocity, Material in specific time OUTPUT : RGB Color Value Physically simulate the flame and make data for rendering

4. Fluid Simulation Get variables of each cell in next time step from data of given time Picture from [Stam99]

5. Navier-Stokes Equation Equation to describe the state of viscous fluid Navier-Stokes Eq. for incompressible fluids was used for simulation

6. Fluid Modeling Amount of moved fluid depends on density and velocity

7. Fluid Modeling Derivative of density is proportional to the amount of transferred gas From equation of ideal gas state

8. Fluid Modeling Because internal energy of gas is time derivative of Temperature is

9. Material Modeling Like the thermal flow, oxygen and fuel flow is

10. Material Modeling According to Chemical Kinetics and Arrhenius’s Equation, the amount of burned fuel is Then energy conservation law gives

11. Get RGB Value from Variables 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 temperature

12. Simulation Scheme Calculate Velocity From Navier-Stokes Equation Calculate Variables Computational Fluid Dynamics Include pressure, density and temperature Compute Fuel’s Burning Effect Temperature Change Emitting Energy Get Light form Cell Get RGB Value Spectrum depends on material property and temperature Intensity depends on emitted energy

13. Volume Rendering 각각의 Cell 을 Volume Rendering 을 사용 Volume 감 있는 Fire Animation 을 표현

14. Volume Rendering 반투명한 GLUT 의 Cube 를 이용해 그리드 의 각 Cell 들의 색상 랜더링 Alpha Blending 시에는 Z-Buffering 에만 의 존할 수 없으므로 시점에 따라 뒤에서부터 그려주게 코드 작성

15. Example [RGB Cube] Different Alpha Channel Value (A= 120, 60, 30, 5) Different Cell Grid Size (N = 10, 20, 50)

16. Demo GRIDSIZE = 10

17. Conclusion Successfully modeled flame physically –But couldn’t find realistic and stable solution –Navier-Stokes Equation Solver should be more stable Rendered explosion

18. Future works Develop more stable CFD Solver Implement Solver for GPGPU Volume Rendering using Ray Casting with GPU

19. 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.wikipedia.org/wiki/Arrhenius_equation, 2006.06.22 현재 ) Keenan Crane et al, Real-Time Simulation and Rendering of 3D Fluids, GPU Gems 3, 633-675, Addison-Wesley Professional, 2007

20. Thank You