Semi-Implicit Interior Penalty Discontinuous Galerkin Methods for Viscous Compressible Flows (Communications in Computational Physics, 2018)
We deal with the numerical solution of the Navier-Stokes equations describing a motion of viscous compressible fluids. In order to obtain a sufficiently stablehigher order scheme with respect to the time and space coordinates, we develop acombination of the discontinuous Galerkin finite element (DGFE) method for the spacediscretization and the backward difference formulae (BDF) for the time discretization.Since the resulting discrete problem leads to a system of nonlinear algebraic equations at each time step, we employ suitable linearizations of inviscid as well as viscousfluxes which give a linear algebraic problem at each time step. Finally, the resultingBDF-DGFE scheme is applied to steady as well as unsteady flows and achieved resultsare compared with reference data.