Modified extended BDF scheme for the discontinuous Galerkin solution of unsteady compressible flows

In this paper, a high-order DG method coupled with a modified extended backward differentiation formulae (MEBDF) time integration scheme is proposed for the solution of unsteady compressible flows. The objective is to assess the performance and the potential of the temporal scheme and to investigate its advantages with respect to the second-order BDF. Furthermore, a strategy to adapt the time step and the order of the temporal scheme based on the local truncation error is considered. The proposed DG-MEBDF method has been evaluated for three unsteady test cases: (i) the convection of an inviscid isentropic vortex; (ii) the laminar flow around a cylinder; and (iii) the subsonic turbulent flow through a turbine cascade.