High-order Discontinuous Galerkin solution of unsteady problems using Modified Extended Backward Differentiation Formulae

This paper presents the results of a high-order Discontinuous Galerkin (DG) method coupled with Modified Extended Backward Differentiation Formulae (MEBDF) for time-dependent compressible flows. The primary objective of this work is to assess the performance of the scheme for a well known inviscid test case as well as to show the potential of this approach in the simulation of a complex turbulent flow through a turbine cascade. The first test case considered is the inviscid isentropic vortex convected on a cartesian grid, for which an exact solution is available. The analysis is performed for three successively refined grids and progressively finer time steps, by using schemes of equal space and time accuracy ranging from 2nd to 4th order. The second test case is the subsonic flow through a turbine cascade which features an unsteady vortex shedding behind the trailing edge of turbine blades. The analysis is performed for a fixed spatial approximation and a fixed time step by considering MEBDF schemes up to 4th order of accuracy.