High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations

Abstract

*† ‡ A high order multidomain spectral difference (SD) method is developed for the three dimensional Navier-Stokes equations on unstructured hexahedral grids. The method is easy to implement since it involves one-dimensional operations only, and does not involve surface or volume integrals. Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner in a unit cube. The concepts of the Riemann solver and high-order local representations are applied to achieve conservation and high order accuracy. In this paper, accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. High order of accuracy and spectral convergence are obtained for the propagation of an isotropic vortex and the Couette flow. The capability of the method for more complex, inviscid and viscous flow problems with curved boundaries is also demonstrated.