Non upwind discontinuous Galerkin schemes for hyperbolic conservation laws in porous media

Discontinuous-Galerkin schemes are presented for convective flow approximation in reservoir simulation. The methods are compared with slope limited MUSCL and TVD schemes. Standard reservoir simulation schemes employ single-point upstream weighting (first order upwind) for approximation of the convective fluxes when multiple phases or components...

A high-order discontinuous Galerkin method for natural convection problems

Discontinuous Galerkin (DG) methods have proved to be very well suited for the construction of robust high-order numerical schemes on unstructured and possibly non conforming grids for a wide variety of problems. In this paper we consider natural convection flow problems and present a high-order DG method for their numerical solution. The...

Semi-implicit discontinuous Galerkin method for the solution of the compressible Navier-Stokes equations

We deal with a numerical solution of the compressible Navier-Stokes equations with the aid of higher order schemes. We employ a combination of the discontinuous Galerkin finite element method for the space semi-discretization and a backward difference formula for the time discretization. Moreover, using a linearization of inviscid as well as...

DG and MUSCL approaches: Comparison of some recent variants

In this preliminary study, we compare the behavior of two classical numerical approaches in compressible fluid dynamics , the MUSCL and the Discontinuous Galerkin (DG) method, applied to aeroacoustics and vortex computation, these two fields being related as noise is often produced from vortex fluctuations. The calculation of the unsteady...

Numerical schemes for compressible flow with all Mach numbers

This work is concerned with the numerical solution of an inviscid compressible flow. Our goal is to develop a sufficiently accurate and robust method allowing the solution of problems with a wide range of Mach numbers. The main ingredients are the discontinuous Galerkin finite element method (DGFEM), semi-implicit time stepping, special...

Stabilization of Kelvin-Helmholtz instabilities in 3D linearized Euler equations using a non-dissipative discontinuous Galerkin method

We present in this paper a time-domain Discontinuous Galerkin dissipation-free method for the transient solution of the three-dimensional linearized Euler equations around a steady-state solution. In the general context of a non-uniform supporting flow, we prove, using the well-known symmetrization of Euler equations, that some aeroacoustic...