Difference Scheme with Adaptive Artificial Viscosity for Gas-Dynamic Computations on Nonuniform Meshes

In this paper, we propose an explicit monotone difference scheme of the second order of approximation for one-dimensional gas dynamics equations. A new method for introducing adaptive artificial viscosity into the difference scheme is proposed. Estimates of the artificial viscosity value are obtained, which is sufficient to monotonize the numerical solution even for discontinuous solutions. When constructing a difference scheme, the possibility of specifying nonuniform distributions of gas-dynamic quantities, as well as nonuniformity of the computational grid with large differences in the geometric dimensions of adjacent computational cells, is also taken into account. Test calculations of the motion of shock waves (SW), contact discontinuities (CD) and rarefaction waves are given. In these test computations, the possibility is shown to obtain highly accurate solutions in using the proposed method.