Algorithm of construction of front of shock waves and contact boundaryes with synthetical viscosity

The work is devoted to research and development of algorithm of construction of front of such waves and contact boundaryes with synthetical viscosity. It is known that calculation of airflow around irregular shaped body using Godunov scheeme with assign front of shock wave movable by normall component of velocity not feasible due to break of front of shock wave. In one's time there were offered many different ways to solve this problem. The simplest way is to move points of the assign front using total velocity. However, such kind of algorithms have no validity from point of view of computational mathematics, because viscosity draged in by such king of algorithms to be beyond all calculation.