Mathematical Foundation of the Optimization-based Fluid Animation Method

Thumbnail Image
Date
2011
Authors
Erleben, Kenny
Misztal, Marek Krzysztof
Bæren, J. Andreas
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
We present the mathematical foundation of a fluid animation method for unstructured meshes. Key contributions not previously treated are the extension to include diffusion forces and higher order terms of non-linear force approximations. In our discretization we apply a fractional step method to be able to handle advection in a numerically simple Lagrangian approach. Following this a finite element method is used for the remaining terms of the fractional step method. The key to deriving a discretization for the diffusion forces lies inrestating the momentum equations in terms of a Newtonian stress tensor. Rather than applying a straightforward temporal finite difference method followed by a projection method to enforce incompressibility as done in the stable fluids method, the last step of the fractional step method is rewritten as an optimization problem to make it easy to incorporate non-linear force terms such as surface tension.
Description

        
@inproceedings{
:10.2312/SCA/SCA11/101-110
,
booktitle = {
Eurographics/ ACM SIGGRAPH Symposium on Computer Animation
},
editor = {
A. Bargteil and M. van de Panne
},
title = {{
Mathematical Foundation of the Optimization-based Fluid Animation Method
}},
author = {
Erleben, Kenny
 and 
Misztal, Marek Krzysztof
 and 
Bæren, J. Andreas
},
year = {
2011
},
publisher = {
The Eurographics Association
},
ISSN = {
1727-5288
},
ISBN = {
978-1-4503-0923-3
},
DOI = {
/10.2312/SCA/SCA11/101-110
}
}
Citation
URI
https://doi.org/10.2312/SCA/SCA11/101-110
Collections
SCA 11: Eurographics/SIGGRAPH Symposium on Computer Animation