High-Order Compressible Flow Simulations with the Unstructured Spectral Difference Method

Abstract

The spectral difference (SD) method is applied to the spatial discretization of the 2-D Euler equations on several compressible flow simulations. An order of accuracy study is performed for schemes from 2nd to 6th order. The work also evaluates a high order hierarchical limiting technique for the SD method. The numerical method results are compared with other high-order methods, such as spectral finite volume and weighted essentially non-oscillatory schemes. Unsteady flow problems with strong shock waves and other discontinuities typical of compressible flows are also analyzed in order to allow for an assessment of the resolution capability and computational cost of the SD scheme along with the applied nonlinear stability technique.

Implicit Spectral Difference Method Solutions of Compressible Flows Considering High-Order Meshes

“…These results are essentially equal to those obtained with explicit time marching scheme discussed in Ref. [19]. The analysis of the actual orders of accuracy obtained with the present implementation of the SD scheme order can be seen in Fig.…”

“…Previous work 19 presented similar results with an explicit time integration scheme. For comparisions, they are shown in Fig.…”

“…therefore with 1/500 of the number of iterations required for convergence of the simulations with an explicit time marching scheme, as discussed in Ref. [19]. In the 3rd-order (p2) simulation with quadratic mesh (q2), each iteration for the implicit scheme lasts from 5 to 10 seconds depending on how much Krylov subiterations were made in the GMRES.…”