On the Connections Between Discontinuous Galerkin and Flux Reconstruction Schemes: Extension to Curvilinear Meshes

摘要: This paper investigates the connections between many popular variants of well-established discontinuous Galerkin method and recently developed high-order flux reconstruction approach on irregular tensor-product grids. We explore these by analysing three nodal versions spectral element approximations types schemes for solving systems conservation laws meshes. demonstrate that existing established regular grids are also valid deformed curved meshes both linear nonlinear problems, provided metric terms accounted appropriately. find aliasing issues arising from nonlinearities either due to a deformed/curved elements or nonlinearity equations equivalent can be addressed using same strategies in approach. In particular, we show when higher-order quadrature rules commonly employed context over- consistent-integration-based dealiasing methods. The found this work help complete picture regarding relations two numerical approaches possibility consistent-integration an manner approaches.