The moving discontinuous Galerkin finite element method with interface condition enforcement for compressible viscous flows

Discontinuous Galerkin Finite Element Method for Inviscid Compressible Flows

This paper presents the development of an algorithm based on the discontinuous Galerkin finite element method (DGFEM) for the Euler equations of gas dynamics. The DGFEM is a mixture of a finite volume and finite element method. In the DGFEM the unknowns in each element are locally expanded in a polynomial series and thus the information about the flow state at the element faces can be directly ...

Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows

Discontinuous Galerkin finite element method for shallow two-phase flows

We present a discontinuous Galerkin finite element method for two depth-averaged two-phase flow models. One of these models contains nonconservative products for which we developed a discontinuous Galerkin finite element formulation in Rhebergen et al. (2008) J. Comput. Phys. 227, 1887-1922. The other model is a new depth-averaged two-phase flow model we introduce for shallow two-phase flows th...

Discontinuous Galerkin Method for Compressible Viscous Reacting Flow

In the present study, a discontinuous Galerkin (DG) framework is developed to simulate chemically reacting flows. The algorithm combines a double-flux method to account for variable thermodynamic properties, a Strang-splitting scheme for the stiff reaction chemistry, a robust WENO-based shock limiter, and the non-linear viscous-diffusive transport is discretized using the BR2 method. The algori...

A discontinuous Galerkin method for viscous compressible multifluids

We present a generalized discontinuous Galerkin method for a multicomponent compressible barotropic Navier-Stokes system of equations. The system presented has a functional viscosity ν which depends on the pressure p = p(ρ, μi) of the flow, with the density ρ and the local concentration μi. High order Runge-Kutta time discretization techniques are employed, and different methods of dealing with...