A reconstructed direct discontinuous Galerkin method for simulating the compressible laminar and turbulent flows on hybrid grids

A reconstructed direct discontinuous Galerkin method is developed and evaluated for simulating the compressible laminar and turbulent flows on hybrid grids. The spatial discretization is implemented through the combination of a highly efficient high-order hybrid reconstructed discontinuous Galerkin method together with a newly developed direct discontinuous Galerkin method for computing viscous fluxes. A variety of typical test cases are selected to evaluate the performance of the proposed hybrid reconstructed direct discontinuous Galerkin method for simulating both laminar flows and turbulent flows. Compared with the traditional discontinuous Galerkin method, the hybrid reconstructed direct discontinuous Galerkin method demonstrates its superior potential of being more accurate and more efficient under the same number of degrees of freedom, thus, shows its promise for further practical applications.