A version of the completely conservative scheme for the gasdynamic equations

An explicit completely conservative scheme of first-order accuracy, stable when Courant's conditions are satisfied, is presented. The scheme is obtained from the problem of the decay of an arbitrary discontinuity and does not require the introduction of mathematical viscosity for calculating shock waves. The results of a calculation of the problem of a plane shock wave and of the laser compression of a sphere of completely ionized hydrogen are presented.