A difference scheme for time-dependent gasdynamic equations based on discontinuous relations in conservative variables

A difference scheme for computing gas flows is proposed. The scheme is based on an approximate non-iterative solution to the Riemann problem. A peculiarity of the scheme is the use of this solution in conservative variables, depending on the breakdown-waves velocities at single jumps. A choice of these velocities is discussed. Our approach ensures the absence of oscillations at gasdynamic jumps and allows one to avoid the difficulties caused by rarefaction zones when characteristics change their signs.