Title: FlowFixer:%20Using%20BFECC%20for%20Fluid%20Simulation
1FlowFixer Using BFECC for Fluid Simulation
ByungMoon Kim Yingjie Liu Ignacio Llamas Jarek
Rossignac Georgia Institute of Technology
2Contents
- Abstract
- Introduction
- Previous Work
- Fluid Simulation
- The BFECC Method
- BFECC for Velocity Advection
- BFECC for Smoke Density and Image Advection
- BFECC for Level Set Advection
- Results
- Conclusion
3Abstract
- Back and Forth Error Compensation and Correction
(BFECC) - Reduce dissipation and diffusion
- First order upwinding or semi-Lagrangian
integration - Second order accuracy both in space and time
- Animation Image advection, Smoke, Water
4Dissipation Example
- The function moves to the left
5Dissipation Example
Interpolation
6Introduction
- Simulation based on Navier-Stokes equation
- Smoke density
- Image advection colored density
- Water level-set
- First order semi-Lagrangian
- Numerical diffusion and dissipation
- Higher order schemes WENO or CIP
7Introduction (Cont)
- BFECC
- Easily
- Very simple
- Combine particle level set method
- Reduced the volume loss
8Previous Work
- Stable fluid 1999
- Semi-Lagrangian treatment
- Visual simulation of smoke 2001
- Smoke simulation
- Vorticity is added
- Practical animation of liquids Animation 2001
- Animation and rendering of complex water surface
- Free surface flows
9Previous Work (Cont)
- Constrained Interpolation Profile CIP
- Yabe and Aoki 1991
- Stable but nondissipative water 2005
- To include velocity and partial derivatives
advecting
10Whats CIP
- Constrained Interpolation Profile
Include partial derivatives
11Previous Work (Cont)
- Particle level-set method
- volume preservation
12The Equations of Flow
- Navier-Stokes equation
- Velocity vector field u (u, v, w)
-
-
??? ???? ???
13Fluid Simulation
Advect term
Diffuse term
Split
Project term
14Fluid Simulation
- Project term
- To solve Poisson equation
15The BFECC Method
- Velocity (u,v,w), density, RGB, level-set
- First order upwinding or semi-Lagrangian
integration
16Implementation of BFECC
17Implementation of BFECC
18BFECC for Velocity Advection
- BFECC needs to be turned off
- Multiphase flow
- To prevent velocities of different fluids
- To prevent different densities
- f lt 5?x
19BFECC for Velocity Advection
small scale details as well as large scale
fluctuations
BFECC in velocity advection on a 80200 grid.
20BFECC for Velocity Advection
The bottom row is simulated with BFECC
The cup tumbles thanks to the reduced damping in
velocity field
21BFECC for Smoke Density and Image Advection
Advection of an image 100250 grid
22BFECC for Smoke Density and Image Advection
bubble rising and bursting
23BFECC for Smoke Density and Image Advection
- To measure the diffusion/dissipation amount
- test problem similar to Zalesaks problem
(800800 grid, CFL 6.29) B original image C
without BFECC time 0.156 sec D with BFECC time
0.36 sec
24BFECC for Level Set Advection
- Redistancing equation
- Semi-Lagrangian style integration
25Whats Redistancing (Reinitialize)
Reinitialize
Air
water
Using Fast-marching Method or Redistancing
equation
26BFECC for Level Set Advection
- Turning redistancing off near the interface
- Following two conditions
27BFECC for Level Set Advection
- First order semi-Lagrangian implementation of
level set advection
Without BFECC
With BFECC To reduced volume loss
28BFECC for Level Set Advection
highly dynamic behavior of water interaction with
air, air bubbles, and solid
Left Without BFECC
Right With BFECC
29Results
- Using PovRay
- To implement the rigid fluid method
- 30 130 seconds per time step on 703 GRID
30Conclusion
- Adding BFECC with a trivial amount of code
- Velocity, smoke density, image or level set
advections - Reducing diffusion and dissipation
- Preserving volume