Two-layer completely conservative gas dynamics schemes with nodal approximation and adaptive regularization of the solution in Euler variables

The paper investigates the stability of a family of two-layer in time completely conservative difference schemes with space-profiled time weights for the system of equations of gas dynamics in Euler variables using adaptive artificial viscosity. Regularization of divergent flows of mass, momentum and internal energy of the equations of gas dynamics using adaptive artificial viscosity that does not violate the properties of complete conservatism of schemes of this class is proposed. Regularized flows make the scheme quasi-monotonic. The results are numerically tested based on Einfeldt problems and shock wave calculations.