A New High-order Spectral Difference Method for Simulating Viscous Flows on Unstructured Grids with Mixed Elements

摘要

In the present study, a new spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. Studies have been performed for the 2D wave equation and the Euler equations. Our present results demonstrated that the spectral-difference Raviart-Thomas (SDRT) method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed-element meshes.