ABSTRACT
We present a higher order numerical scheme developed for the simulation of unsteady inviscid compressible flow. This scheme is based on a combination of the discontinuous Galerkin method for a space semi-discretization and the backward difference formula for a time discretization. We employ a suitable linearization of inviscid fluxes, then linear terms are discretized implicitly whereas nonlinear ones by an explicit extrapolation, which preserve a high order of accuracy and leads to a linear problem at each time step. Moreover, we discuss a use of nonreflecting boundary conditions at inflow/outflow parts of boundary, present a stabilization technique which avoid spurious oscillations of numerical solution in vicinity of shock waves and mention an adaptive strategy of a choice of the time step. Finally, several numerical examples of steady as well as unsteady flows demonstrating an efficiency of the scheme is presented.
