Grid-optimized dispersion-relation-preserving schemes for non-uniform cartesian grids

When the classic Dispersion-Relation-Preserving (DRP) scheme is applied to practical problems using non-uniform grids, spurious numerical oscillations and instabilities will be excited due to the inherent lacking of numerical dissipation. A Grid-Optimized Dispersion-Relation-Preserving (GODRP) scheme for non-uniform grids was proposed by Cheong and Lee to remedy this problem. In this paper, the derivation and formulation of the GODRP scheme were improved for non-uniform Cartesian grids in a more general form. To show the characteristics of the improved GODRP scheme, a 2-D initial pulse problem was solved on an extremely non-uniform Cartesian mesh using both the GODRP scheme and the DRP scheme. Numerical results indicate that because of the inherent numerical dissipation, the GODRP scheme is more feasible to be applied to the aeroacoustic problems using the non-uniform Cartesian grids, and the enhancement of computation accuracy can be expected.