基于非结构网格间断有限元方法在可压缩流体中的应用

Application of Discontinuous Galerkin Methods Based on Unstructured Grids for Compressible Viscous Flows

本文开发了一套基于非结构网格的间断有限元方法(DG)程序,并对与单元形状无关的斜率限制器进行了研究。此程序支持多种网格类型,能够方便应用于具有混合单元的非结构网格,具有处理复杂几何结构的能力,为研究叶轮机械内部复杂流动现象提供了有效的研究工具。本文利用该程序对若干典型无黏和黏性问题进行数值模拟,结果表明,该程序具有较高的可信度,能够处理具有混合单元的非结构网格,并给出良好的数值模拟结果。

An unstructured-grid code based on the discontinuous Galerkin method is developed and an element-adaptive slope limiter is investigated in this paper.Various types of elements can be used in this code,leading to a versatile method on arbitrary unstructured grids.Thus,this method can be used to resolve problems with complex geometries and can be used to investigate the complicated phenomena in turbomachinery.Several Euler and viscous flow problems are simulated herein and the results show its superior performance for solving compressible flow problems with complex geometries.