Numerical modeling of elliptic equations on unstructured grids (Journal of Mathematics Mechanics and Computer Science, 2018)
time, many application tasks require calculations in areas with complex geometry. Descriptionof 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 largepreference was given for methods that can be applied on unstructured grids. This method is a finitevolume method. One of the advantages of this method is performing of local and global conservationlaws, and this is very important in solving many applied problems. In the present work the varietyof nets with their advantages and disadvantages are described, also the final volume method andchoice of the shape of final volume are considered, discretization of the Poisson equation by finitevolume method is made on the structural grid, formulas of finding areas, volumes and normal aredescribed 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-dimensionalcases on unstructured and hybrid grid. Finally, numerical results for unstructured and hybridgrids, as well as the data that obtained are compared with the analytical results, which showsgood agreement. The numerical values are illustrated in the work in the form of plots.
Keywords: Poisson equation; unstructured mesh; hybrid mesh; finite volume method