The paper concerns with a modification of adaptive artificial viscosity technique for constructing gas-dynamic difference schemes in spherical coordinates, which allow performing numerical calculations with a sufficiently high resolution of the flow structure using regular as well as irregular difference meshes. Homogeneous conservative difference schemes of gas dynamics in spherical geometry for a one-dimensional statement of the problem are constructed. Estimates of the value of adaptive artificial viscosity that guarantees the monotonicity of the difference solution are obtained. The estimates take into account both the heterogeneity of gas-dynamic quantities in the computational domain and the mesh unevenness. Numerical calculations for testing the technique are performed on a model problem. The calculation results demonstrate the possibility of obtaining highly accurate solutions when using irregular meshes.
Krukovskii et al. (Mon,) studied this question.