Numerical simulations of compressible mixing layers with a discontinuous Galerkin method

Abstract

Discontinuous Galerkin (DG) method is known to have several advantages for flow simulations, in particular, in flexible accuracy management and adaptability to mesh refinement. In the present work, the DG method is developed for numerical simulations of both temporally and spatially developing mixing layers. For the temporally developing mixing layer, both the instantaneous flow field and time evolution of momentum thickness agree very well with the previous results. Shocklets are observed at higher convective Mach numbers and the vortex paring manner is changed for high compressibility. For the spatially developing mixing layer, large-scale coherent structures and self-similar behavior for mean profiles are investigated. The instantaneous flow field for a three-dimensional compressible mixing layer is also reported, which shows the development of large-scale coherent structures in the streamwise direction. All numerical results suggest that the DG method is effective in performing accurate numerical simulations for compressible shear flows.