A hybrid mixed method for the compressible Navier-Stokes equations

Authors:
Jochen SchüTz;Georg May
Affiliations:
IGPM, RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany;AICES Graduate School, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany
Venue:
Journal of Computational Physics
Year:
2013

Citing 7
Cited 0

TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems

Journal of Computational Physics
A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations

Journal of Computational Physics
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

SIAM Journal on Numerical Analysis
A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems

SIAM Journal on Numerical Analysis
Adjoint Consistency Analysis of Discontinuous Galerkin Discretizations

SIAM Journal on Numerical Analysis
An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations

Journal of Computational Physics
An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations

Journal of Computational Physics

Quantified Score

Hi-index	31.45

Visualization

Abstract

We present a novel discretization method for nonlinear convection-diffusion equations and, in particular, for the compressible Navier-Stokes equations. The method is based on a Discontinuous Galerkin (DG) discretization for convection terms, and a Mixed method using H (div) spaces for the diffusive terms. Furthermore, hybridization is used to reduce the number of globally coupled degrees of freedom. For the scalar case, a local postprocessing procedure is used to enhance the quality of the approximate solution w"h. The method reduces to a DG scheme for pure convection, and to a Mixed method for pure diffusion, while for the intermediate case the combined variational formulation requires no additional parameters. We formulate and validate our scheme for nonlinear model problems, as well as compressible flow problems.