求解对流扩散方程的一种高分辨率有限体积-有限元方法

A high-resolution finite volume-finite element method for convection-diffusion equations

此文研究在无结构三角网格上求解对流扩散方程的有限体积-有限元方法,设计了一种新的适合于多边形作为控制体的顶点中心型的二维无结构网格方法的vanAlbada型限制器函数,并在此基础上给出了一种新的求解对流扩散方程的有限体积-有限元方法。数值实验结果表明,此文给出的van Albada型限制器函数有效地改进了多边形作为控制体的顶点中心型的有限体积法的收敛性能,给出的求解对流扩散方程的有限体积-有限元方法在精确度上有明显改进。

In this paper, a high-resolution finite volume-finite element （FV-FE） solution of the convection-diffusion problems on unstructured triangular meshes was considered. A new van Albada-type slope limiter was presented which was devised for the polygonal control volume and was used in the cell-vertex finite volume method. Then, a novel FV-FE method for convection-diffusion equations was developed. The numerical simulations show that, the proposed van Albada-type slope limiter does not stall convergence of the cell-vertex finite volume method as many other slope limiters do. The results obtained by the proposed FV-FE method for the convection-diffusion equations have been much improved in accuracy.