Optimization-based Fluid Simulation on Unstructured Meshes

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Date
2010
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Volume Title
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The Eurographics Association
Abstract
We present a novel approach to fluid simulation, allowing us to take into account the surface energy in a precise manner. This new approach combines a novel, topology-adaptive approach to deformable interface tracking, 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 tetrahedralization 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 controllable 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 inclusion 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.
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@inproceedings{
:10.2312/PE/vriphys/vriphys10/011-020
, booktitle = {
Workshop in Virtual Reality Interactions and Physical Simulation "VRIPHYS" (2010)
}, editor = {
Kenny Erleben and Jan Bender and Matthias Teschner
}, title = {{
Optimization-based Fluid Simulation on Unstructured Meshes
}}, author = {
Misztal, Marek Krzysztof
and
Bridson, Robert
and
Erleben, Kenny
and
Bærentzen, Jakob Andreas
and
Anton, François
}, year = {
2010
}, publisher = {
The Eurographics Association
}, ISBN = {
978-3-905673-78-4
}, DOI = {
/10.2312/PE/vriphys/vriphys10/011-020
} }
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