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|Title:||Evaluating finite element methods for the level set equation|
|Authors:||Farthing, Matthew W.|
Kees, Christopher E.
Volume of fluid
Computational fluid dynamics
|Publisher:||Coastal and Hydraulics Laboratory (U.S.)|
Engineer Research and Development Center (U.S.)
|Series/Report no.:||ERDC/CHL TR ; 09-11.|
We review the formulation of multiscale-stabilized conforming (CG) and discontinuous Galerkin (DG) finite element methods for scalar hyperbolic partial differential equations (PDEs) in the PyADH framework. In addition, we consider simple extensions of a recently introduced DG scheme for Hamilton-Jacobi equations (Cheng and Shu, 2007) to simplicial meshes. We investigate these methods’ performance for several linear and nonlinear problems with the goal of identifying efficient techniques for resolving sharp interfaces on unstructured meshes. We pay particular attention to the level set equation in order to evaluate the suitability of these techniques for extending finite element-based incompressible Navier-Stokes codes like ADH to full two-phase flow via level set formulations.
|Appears in Collections:||Technical Report|