Mathematical foundation of the optimization-based fluid animation method

TY - GEN

T1 - Mathematical foundation of the optimization-based fluid animation method

AU - Erleben, Kenny

AU - Misztal, Marek Krzysztof

AU - Bærentzen, Jakob Andreas

PY - 2011

Y1 - 2011

N2 - 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 in restating 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.

AB - 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 in restating 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.

KW - computational fluid dynamics, deformable simplicial complexes, diffusion forces, finite element method, optimization-based fluid animation, unstructured meshes

U2 - 10.1145/2019406.2019420

DO - 10.1145/2019406.2019420

M3 - Article in proceedings

SN - 978-1-4503-0923-3

SP - 101

EP - 110

BT - Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation

A2 - Spencer , Stephen N.

PB - Association for Computing Machinery

T2 - ACM/Eurographics Symposium on Computer Animation 2011

Y2 - 5 August 2011 through 7 August 2011

ER -