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Energy-preserving integrators for fluid animation with discrete exterior calculus on two-dimensional meshes

: Grasser, Tim
: Stork, André; Weber, Daniel

Darmstadt, 2012, 53 pp.
Darmstadt, TU, Bachelor Thesis, 2012
Bachelor Thesis
Fraunhofer IGD ()
computational fluid dynamics (CFD); discrete exterior calculus (DEC)

In the last decades a lot of approaches have been developed for implementing computational fluid dynamics (CFD) in the computer graphics community. One of the new approaches in fluid simulations is the discrete exterior calculus (DEC). DEC uses well-centered meshes to describe its integration space. Mullen et al. [MCP+09] introduced 2009 a new integration scheme based on DEC and the Navier-Stokes equations that preserves mass by definition of DEC. His discrete formulation of the Navier-Stokes equations provides full control about viscosity and moreover an almost perfect preservation of kinetic energy.
We translate Mullens discretization into two dimensions and extend it to regular girds. We will discuss how to manage non-trivial boundary conditions. Finally we will analyze the results of Mullens approach, and analyze alternative methods to further improve those results.