Development of the Method of Adaptive Artificial Viscosity for Fluid Dynamics Computations on Nonuniform Difference Grids

The method of adaptive artificial viscosity is generalized to construct difference schemes for fluid dynamics that ensure high resolution of the structure of flows both on uniform and nonuniform grids. Difference schemes approximating the one-dimensional system of fluid dynamics equations are considered. Bounds on the magnitude of adaptive viscosity obtained in this paper take into account the nonuniformity of the distribution of gas-dynamic quantities in the computational domain and the nonuniformity of the difference grid. The constructed schemes with adaptive artificial viscosity are homogeneous and conservative. These schemes are evaluated on model problems the solutions to which describe various smooth gas-dynamic structures, as well as strong and weak discontinuities. The possibility of obtaining highly accurate solutions on grids with significant difference of geometric size of adjacent difference cells is demonstrated.