非结构网格的高精度有限体积离散格式

HIGH RESOLUTION FINITE VOLUME SCHEMES FOR DISCRETIZATION OF CONVECTION ON UNSTRUCTURED MESH

本文针对单元中心非结构网格有限体积算法,通过构造上游虚节点和局部一维坐标,将结构化网格中常用的规正变量(NVSF)和总变差消失通量限制器(TVD FL)两种形式的传统高精度格式移植到非结构网格中。为了提高虚节点的插值精度,使用最小二乘法计算单元中心的变量梯度。经典算例考核并与商业软件FLUENT结果的比较表明,本文对非结构网格的高精度格式移植成功有效。

In this paper, widely used high resolution schemes for structured grids in either the NVSF （normalized variable and space formulation） or the TVD （total variation diminishing） FL （flux limiter） forms are implemented to the cell-centered unstructured meshes by constructing a local coordinate and introducing a virtual upstream node. In order to improve the accuracy of interpolation, a least mean square method is employed to calculate the gradient. The method developed in this paper is validated against the benchmark numerical solution of a lid-driven cavity flow; comparison with the results of a commercial package, the FLUENT, is also carried out.