Generation of two- and three-dimensional grids for problems of gas dynamics on the basis of the Poisson equation (Q1390387)

For the grid generation, we use the vector Poisson equation which is approximated by finite differences (for the first and second derivatives we use symmetric differences). The obtained system of linear equations is solved by a simple iteration method. We use as the boundary conditions either the Dirichlet boundary condition or the Neumann boundary condition. In the second of cases, the grid generated by means of Poisson equation is orthogonal to the part of boundary where the Neumann boundary condition is given. By means of described algorithm we generate two-dimensional grids for analysis of two-dimensional plane and axially symmetric problems of the gas dynamics.