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

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

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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

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Dissipation Example

• The function moves to the left

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Dissipation Example

• To appear dissipation

Interpolation
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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

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Introduction (Cont)

• BFECC
• Easily
• Very simple
• Combine particle level set method
• Reduced the volume loss

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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

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Previous Work (Cont)

• Constrained Interpolation Profile CIP
• Yabe and Aoki 1991
• Stable but nondissipative water 2005
• To include velocity and partial derivatives
  advecting

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Whats CIP

• Constrained Interpolation Profile

Include partial derivatives
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Previous Work (Cont)

• Particle level-set method
• volume preservation

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The Equations of Flow

• Navier-Stokes equation
• Velocity vector field u (u, v, w)
• 
  

??? ???? ???
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Fluid Simulation
Advect term
Diffuse term
Split
Project term
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Fluid Simulation

• Project term
• To solve Poisson equation

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The BFECC Method

• Velocity (u,v,w), density, RGB, level-set

• First order upwinding or semi-Lagrangian
  integration

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Implementation of BFECC

• BFECC is implemented as

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Implementation of BFECC
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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

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

The bottom row is simulated with BFECC
The cup tumbles thanks to the reduced damping in
velocity field
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BFECC for Smoke Density and Image Advection
Advection of an image 100250 grid
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BFECC for Smoke Density and Image Advection
bubble rising and bursting
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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
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BFECC for Level Set Advection

• Redistancing equation
• Semi-Lagrangian style integration

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Whats Redistancing (Reinitialize)
Reinitialize
Air
water
Using Fast-marching Method or Redistancing
equation
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BFECC for Level Set Advection

• Turning redistancing off near the interface
• Following two conditions

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BFECC for Level Set Advection

• First order semi-Lagrangian implementation of
  level set advection

Without BFECC
With BFECC To reduced volume loss
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BFECC for Level Set Advection
highly dynamic behavior of water interaction with
air, air bubbles, and solid
Left Without BFECC
Right With BFECC
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Results

• Using PovRay
• To implement the rigid fluid method
• 30 130 seconds per time step on 703 GRID

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Conclusion

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