非均匀笛卡尔坐标系网格优化频散相关保持格式研究

为克服传统频散相关保持格式 (即 DRP格式 )在数值求解非均匀网格问题时由于寄生波的产生而导致的数值不稳定的问题 ,Cheong &Lee提出了一种网格优化频散相关保持格式 (即 GODRP格式 )。根据其优化思想 ,在非均匀笛卡尔坐标系网格条件下 ,推导得到了更为通用的 GODRP格式优化系数公式。针对 Cheong&Lee文中算例比较不是在同一基准上进行的不足之处 ,设计了一个极端恶劣条件下的非均匀笛卡尔网格 ,采用 GODRP格式和 DRP格式分别求解了二维初始扰动波传播的算例。计算结果表明 ,由于 GODRP格式具有与网格相关的自带粘性 ,不用再另外加入人工粘性便可获得精度较高的数值结果 ,避免了传统 DRP格式在给定粘性时人为经验的影响因素。对于非均匀笛卡尔网格 ,GODRP格式确实比传统 DRP格式更加通用 ,并可以得到更为准确的数值模拟效果 

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 & 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.