Optimization-based fluid simulation on unstructured meshes

TY - GEN

T1 - Optimization-based fluid simulation on unstructured meshes

AU - Misztal, Marek Krzysztof

AU - Bridson, Robert

AU - Erleben, Kenny

AU - Bærentzen, Jakob Andreas

AU - Anton, Francois

N1 - Conference code: 7

PY - 2010

Y1 - 2010

N2 - We present a novel approach to fluid simulation, allowing us to take into account the surface energy in a pre- cise manner. This new approach combines a novel, topology-adaptive approach to deformable interface track- ing, called the deformable simplicial complexes method (DSC) with an optimization-based, linear finite element method for solving the incompressible Euler equations. The deformable simplicial complexes track the surface of the fluid: the fluid-air interface is represented explicitly as a piecewise linear surface which is a subset of tetra- hedralization of the space, such that the interface can be also represented implicitly as a set of faces separating tetrahedra marked as inside from the ones marked as outside. This representation introduces insignificant and con- trollable numerical diffusion, allows robust topological adaptivity and provides both a volumetric finite element mesh for solving the fluid dynamics equations as well as direct access to the interface geometry data, making in- clusion of a new surface energy term feasible. Furthermore, using an unstructured mesh makes it straightforward to handle curved solid boundaries and gives us a possibility to explore several fluid-solid interaction scenarios.

AB - We present a novel approach to fluid simulation, allowing us to take into account the surface energy in a pre- cise manner. This new approach combines a novel, topology-adaptive approach to deformable interface track- ing, called the deformable simplicial complexes method (DSC) with an optimization-based, linear finite element method for solving the incompressible Euler equations. The deformable simplicial complexes track the surface of the fluid: the fluid-air interface is represented explicitly as a piecewise linear surface which is a subset of tetra- hedralization of the space, such that the interface can be also represented implicitly as a set of faces separating tetrahedra marked as inside from the ones marked as outside. This representation introduces insignificant and con- trollable numerical diffusion, allows robust topological adaptivity and provides both a volumetric finite element mesh for solving the fluid dynamics equations as well as direct access to the interface geometry data, making in- clusion of a new surface energy term feasible. Furthermore, using an unstructured mesh makes it straightforward to handle curved solid boundaries and gives us a possibility to explore several fluid-solid interaction scenarios.

U2 - 10.2312/PE/vriphys/vriphys10/011-020

DO - 10.2312/PE/vriphys/vriphys10/011-020

M3 - Article in proceedings

SN - 978-3-905673-78-4

SP - 11

EP - 20

BT - Workshop in Virtual Reality Interactions and Physical Simulation "VRIPHYS" (2010)

A2 - Erleben, Kenny

A2 - Bender, Jan

A2 - Teschner, Matthias

PB - Eurographics Association

T2 - 7th Workshop on Virtual Reality Interaction and Physical Simulation

Y2 - 11 November 2010 through 12 November 2010

ER -