Numerical modeling of elliptic equations on unstructured grids

Abstract

time, many application tasks require calculations in areas with complex geometry. Description
of computational areas with complex geometric shape is best performed on unstructured grids.
An important advantage of unstructured grid is simplicity of generation. For this purpose a large
preference was given for methods that can be applied on unstructured grids. This method is a finite
volume method. One of the advantages of this method is performing of local and global conservation
laws, and this is very important in solving many applied problems. In the present work the variety
of nets with their advantages and disadvantages are described, also the final volume method and
choice of the shape of final volume are considered, discretization of the Poisson equation by finite
volume method is made on the structural grid, formulas of finding areas, volumes and normal are
described and displayed. The aim of this work is the further application of the finite volume method,
and obtaining approximation of the Poisson equation in two-dimensional and three-dimensional
cases on unstructured and hybrid grid. Finally, numerical results for unstructured and hybrid
grids, as well as the data that obtained are compared with the analytical results, which shows
good agreement. The numerical values are illustrated in the work in the form of plots.