Abstract
The spectral difference (SD) method is a new high-order method for unstructured grids proposed recently by Liu et al. (2006). In this paper, a two dimensional computation aeroacoustics (CAA) tool based on SD method is developed. Five Riemann solvers are implemented in the current code, including Roe scheme, advection upstream splitting method (AUSM), flux-vector-splitting scheme, Rusanov scheme, convective upwind and split pressure (CUSP) scheme. A comparison of these Riemann solvers is carried out with three CAA workshop benchmark problems. The relative error of each solver in simulating of entropy, vorticity and acoustic waves is presented. The accuracy of the SD method with each Riemann solver is obtained. It is found that the usually used Rusanov scheme is less accurate than other solvers. AUSM and CUSP schemes are more accurate than others in simulating acoustic waves. Meanwhile, the effect of mesh quality on the accuracy of SD method is investigated. Gaussian distributed random error is superimposed on a base mesh to change the mesh quality. The accuracy of each solver on the skewed mesh is presented and compared with the results on base mesh. It is shown that mesh quality has little effect on the accuracy of SD method if the mesh resolution is sufficient.
Published Version
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