High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations on Unstructured Hexahedral Grids (Communications in Computational Physics, 2018)
A high order multidomain spectral difference method has been developedfor 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 aunit cube. The concepts of the Riemann solver and high-order local representationsare applied to achieve conservation and high order accuracy. In this paper, accuracystudies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. High order of accuracy and spectral convergence areobtained for the propagation of an isotropic vortex and Couette flow. The capabilityof the method for both inviscid and viscous flow problems with curved boundaries isalso demonstrated.
Keywords: High order; unstructured grids; spectral difference; Navier-Stokes.