Publications

Control Volume Finite Element Method with Multidimensional Edge Element Scharfetter-Gummel upwinding. Part 2. Computational Study

Peterson, Kara J.; Bochev, Pavel B.

In [3] we proposed a new Control Volume Finite Element Method with multi-dimensional, edge- based Scharfetter-Gummel upwinding (CVFEM-MDEU). This report follows up with a detailed computational study of the method. The study compares the CVFEM-MDEU method with other CVFEM and FEM formulations for a set of standard scalar advection-diffusion test problems in two dimensions. The first two CVFEM formulations are derived from the CVFEM-MDEU by simplifying the computation of the flux integrals on the sides of the control volumes, the third is the nodal CVFEM [2] without upwinding, and the fourth is the streamline upwind version of CVFEM [10]. The finite elements in our study are the standard Galerkin, SUPG and artificial diffusion methods. All studies employ logically Cartesian partitions of the unit square into quadrilateral elements. Both uniform and non-uniform grids are considered. Our results demonstrate that CVFEM-MDEU and its simplified versions perform equally well on rectangular or nearly rectangular grids. However, performance of the simplified versions significantly degrades on non-affine grids, whereas the CVFEM-MDEU remains stable and accurate over a wide range of mesh Peclet numbers and non-affine grids. Compared to FEM formulations the CVFEM-MDEU appears to be slightly more dissipative than the SUPG, but has much less local overshoots and undershoots.