三维谱差分格式非结构混合网格求解方法

High-Order Spectral Difference Method on 3D Unstructured Grids via Mixed Elements

高精度方法在多种网格单元上的推进是一个难点。提出了一种基于高精度谱差分格式(SD)的三维混合网格求解方法,用于求解三棱柱/四面体混合网格。通过一阶h-加密方法对混合网格进行加密,生成一套六面体网格,并保证网格在边界处的高阶精度。将设计于六面体单元上的SD格式应用于加密后的非结构网格。通过计算Euler Vortex流动以及Taylor-Couette流动,验证了求解器对于无黏和有黏流动的高精度特性;通过定常球体绕流数值模拟以及非定常三维圆柱绕流数值模拟,与现有文献结果进行对比,验证了方法的有效性。

The high-order methods is difficultly applied in various elements. The development of a 3D solver by using the spectral difference method of unstructured grids via mixed elements is presented. A mixed tri-prism and tetrahedral grid is firstly refined using one-level h-refinement to generate a hexahedral grid while keeping the curvature of wall boundaries. The SD method designed for hexahedral elements can subsequently be applied for refining the unstructured grid. Through a series of numerical tests, the present method is high-order accurate for both inviscid and viscous flows is demonstrated;the results obtained for inviscid and viscous compressible flows compare well with other published results.