A comparison of computational efficiencies of spectral difference method and correction procedure via reconstruction

We report computational efficiencies of two types of numerical solvers. The first type uses the spectral difference (SD) method and the second one uses the correction procedure via reconstruction (CPR). In this paper, we employ the lumped g2g2 scheme proposed by Huynh as an example of the CPR approach. The solvers deal with both inviscid Euler equations and Navier–Stokes equations on 2D unstructured grids which are comprised of all quadrilateral cells. Both types of solvers are programmed using Fortran 90 with similar management of data structures. We employ identical time marching schemes for both SD and CPR methods. Spatial 3rd and 4th order of accuracy for both methods is demonstrated by a study of a moving inviscid vortex. The comparisons were directed to measure the computational efficiency of both SD and CPR methods in spatial discretization. With respect to the fourth order methods, CPR is 27% faster than SD for inviscid flow, and more promisingly, CPR is over 40% faster than SD for viscous flow.