Model Gas-Dynamical Problems Possessing Cylindrical and Spherical Symmetry and Their Solution with the Aid of Weno Schemes

The solution of a number of problems of gas dynamics that are associated with cylindrically and spherically symmetric nonstationary compression of an inviscid gas is considered. Discretization of the Euler equations is carried out with the aid of the method of finite volumes and difference schemes of the WENO type. The results of numerical simulation are compared with exact solutions and with the results of the calculations available in the literature. The solutions of two- and three-dimensional problems possessing cylindrical and spherical symmetry are given in comparison with the solutions obtained in one-dimensional formulation. The calculations with the use of WENO schemes make it possible to obtain an exact and monotonic solution of the problem in the presence of both weak and strong gas-dynamical discontinuities.