FlowFixer: Using BFECC for Fluid Simulation

ByungMoon Kim Yingjie Liu Ignacio Llamas Jarek Rossignac

Georgia Institute of Technology

ContentsContents

• 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

AbstractAbstract

• 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

Dissipation Example Dissipation Example

• The function moves to the left

Dissipation Example Dissipation Example

• To appear dissipation

Interpolation

IntroductionIntroduction

• 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

Introduction Introduction (Con’t)

• BFECC

– Easily

– Very simple

• Combine particle level set method

– Reduced the volume loss

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

Previous Work (Con’t)

• Constrained Interpolation Profile [CIP]– Yabe and Aoki [1991]

– Stable but nondissipative water [2005]

– To include velocity and partial derivatives advecting

What’s CIPWhat’s CIP

• Constrained Interpolation Profile

Include partial derivatives

Previous Work (Con’t)

• Particle level-set method– volume preservation

Particle Level-set Method

컴퓨터 그래픽스 연구실

The Equations of FlowThe Equations of Flow

• Navier-Stokes equation

– Velocity vector field u = (u, v, w)

0 u

u p f t

: velocity : density : pressure

: viscosity : external force : time step

fuuuu

2v

p

t

Fluid Simulation

fuuuu

p

vt )()(

fuuuuu

)()(* nnn

n

t

p

t

n

*uu

*2 u

t

p

ptn

*1 uu

Split

Project term

Advect term Diffuse term

Fluid Simulation

*2 u

t

p

• Project term

– To solve Poisson equation

The BFECC Method

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

• First order upwinding or semi-Lagrangian integration

Implementation of BFECC

• BFECC is implemented as:

Implementation of BFECC

~n 1~ n ~

BFECC for Velocity Advection

• BFECC needs to be turned off

– Multiphase flow

– To prevent velocities of different fluids

– To prevent different densities

– |φ| < 5∆x

BFECC for Velocity Advection

BFECC in velocity advection on a 80×200 grid.

small scale details as well as large scale fluctuations

BFECC for Velocity Advection

The bottom row is simulated with BFECCThe cup tumbles thanks to the reduced damping in velocity field

BFECC for Smoke Density and Image Advection

Advection of an image100×250 grid

BFECC for Smoke Density and Image Advection

bubble rising and bursting

BFECC for Smoke Density and Image Advection

• To measure the diffusion/dissipation amount

– test problem similar to Zalesak’s problem

(800×800 grid, CFL = 6.29)B : original imageC: without BFECC time 0.156 secD: with BFECC time 0.36 sec

BFECC for Level Set Advection

• Redistancing equation

• Semi-Lagrangian style integration

What’s Redistancing (Reinitialize)What’s Redistancing (Reinitialize)

0

0Reinitialize

water

Air

0

Using Fast-marching Method orRedistancing equation

BFECC for Level Set Advection

• Turning redistancing off near the interface

• Following two conditions

BFECC for Level Set Advection

• First order semi-Lagrangian implementation of level set advection

Without BFECC With BFECCTo reduced volume loss

BFECC for Level Set Advection

Left : Without BFECC

Right : With BFECC

highly dynamic behaviorof water interaction with air, air bubbles, and solid

Results

• Using PovRay

• To implement the rigid fluid method

• 30 ~130 seconds per time step on 703 GRID

• Adding BFECC with a trivial amount of code

– Velocity, smoke density, image or level set advections

– Reducing diffusion and dissipation

– Preserving volume

Conclusion