Adaptive artificial viscosity method for the numerical solution of hyperbolic equations and systems

In this paper, the rationale for the adaptive artificial viscosity method (AAV) for solving hyperbolic equations and systems is given. The algorithm for applying the AIV method is described in detail on the example of a system of equations of gas dynamics. Numerical solutions are carried out for the problem of decay of a discontinuity in a one-dimensional and two-dimensional formulation.