A conservative discontinuous Galerkin scheme for the 2D incompressible Navier--Stokes equations

Lukas Einkemmer; Matthias Wiesenberger

doi:10.1016/j.cpc.2014.07.007

A conservative discontinuous Galerkin scheme for the 2D incompressible Navier--Stokes equations

Computational Physics 2017-01-06 v1 Numerical Analysis Numerical Analysis Fluid Dynamics Plasma Physics

Authors: Lukas Einkemmer , Matthias Wiesenberger

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Abstract

In this paper we consider a conservative discretization of the two-dimensional incompressible Navier--Stokes equations. We propose an extension of Arakawa's classical finite difference scheme for fluid flow in the vorticity-stream function formulation to a high order discontinuous Galerkin approximation. In addition, we show numerical simulations that demonstrate the accuracy of the scheme and verify the conservation properties, which are essential for long time integration. Furthermore, we discuss the massively parallel implementation on graphic processing units.

Keywords

discontinuous Galerkin scheme incompressible Navier-Stokes equations vorticity-stream function formulation conservation properties Arakawa scheme GPU parallel implementation

Cite

@article{arxiv.1311.7477,
  title  = {A conservative discontinuous Galerkin scheme for the 2D incompressible Navier--Stokes equations},
  author = {Lukas Einkemmer and Matthias Wiesenberger},
  journal= {arXiv preprint arXiv:1311.7477},
  year   = {2017}
}

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