The discontinuous Galerkin spectral element methods for compressible flows on two-dimensional mixed grids

摘要: Abstract This paper presents a practical algorithm for constructing high order discontinuous Galerkin spectral element methods (DGSEM) on mixed triangular and quadrilateral grids. The traditional DGSEM belongs to the collocation-type nodal method which is computationally efficient one-dimensional tensor-product work generalizes grids using symmetric quadrature points in sphere close packed arrangement. dispersion dissipation analysis shows that scheme stable linear problems triangles. A problem independent limiting procedure proposed capturing shock waves. main components are modified KXRCF detector, smoothness indicator high-resolution WENO limiter based candidate polynomials constructed by newly developed projection approach. implementation of also presented. Numerical examples verify scheme's accuracy robustness computing inviscid viscous compressible flows.