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FlowFixer:%20Using%20BFECC%20for%20Fluid%20Simulation

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Reduce dissipation and diffusion. First order upwinding or semi-Lagrangian integration ... To measure the diffusion/dissipation amount. test problem similar to ... – PowerPoint PPT presentation

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Title: FlowFixer:%20Using%20BFECC%20for%20Fluid%20Simulation


1
FlowFixer Using BFECC for Fluid Simulation
ByungMoon Kim Yingjie Liu Ignacio Llamas Jarek
Rossignac Georgia Institute of Technology
2
Contents
  • 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

3
Abstract
  • 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

4
Dissipation Example
  • The function moves to the left

5
Dissipation Example
  • To appear dissipation

Interpolation
6
Introduction
  • 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

7
Introduction (Cont)
  • BFECC
  • Easily
  • Very simple
  • Combine particle level set method
  • Reduced the volume loss

8
Previous 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

9
Previous Work (Cont)
  • Constrained Interpolation Profile CIP
  • Yabe and Aoki 1991
  • Stable but nondissipative water 2005
  • To include velocity and partial derivatives
    advecting

10
Whats CIP
  • Constrained Interpolation Profile

Include partial derivatives
11
Previous Work (Cont)
  • Particle level-set method
  • volume preservation

12
The Equations of Flow
  • Navier-Stokes equation
  • Velocity vector field u (u, v, w)


??? ???? ???
13
Fluid Simulation
Advect term
Diffuse term
Split
Project term
14
Fluid Simulation
  • Project term
  • To solve Poisson equation

15
The BFECC Method
  • Velocity (u,v,w), density, RGB, level-set
  • First order upwinding or semi-Lagrangian
    integration

16
Implementation of BFECC
  • BFECC is implemented as

17
Implementation of BFECC
18
BFECC 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

19
BFECC for Velocity Advection
small scale details as well as large scale
fluctuations
BFECC in velocity advection on a 80200 grid.
20
BFECC for Velocity Advection

The bottom row is simulated with BFECC
The cup tumbles thanks to the reduced damping in
velocity field
21
BFECC for Smoke Density and Image Advection
Advection of an image 100250 grid
22
BFECC for Smoke Density and Image Advection
bubble rising and bursting
23
BFECC 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
24
BFECC for Level Set Advection
  • Redistancing equation
  • Semi-Lagrangian style integration

25
Whats Redistancing (Reinitialize)
Reinitialize
Air
water
Using Fast-marching Method or Redistancing
equation
26
BFECC for Level Set Advection
  • Turning redistancing off near the interface
  • Following two conditions

27
BFECC for Level Set Advection
  • First order semi-Lagrangian implementation of
    level set advection

Without BFECC
With BFECC To reduced volume loss
28
BFECC for Level Set Advection
highly dynamic behavior of water interaction with
air, air bubbles, and solid
Left Without BFECC
Right With BFECC
29
Results
  • Using PovRay
  • To implement the rigid fluid method
  • 30 130 seconds per time step on 703 GRID

30
Conclusion
  • Adding BFECC with a trivial amount of code
  • Velocity, smoke density, image or level set
    advections
  • Reducing diffusion and dissipation
  • Preserving volume
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