A TRACKING METHOD FOR GAS-FLOW INTO VACUUM BASED ON THE VACUUM RIEMANN PROBLEM

In this paper, a tracking method is proposed for the expansion of gas flow into vacuum which may be combined with numerical methods for the equations of gas dynamics, the Euler equations. This tracking prevents the difficulties of the numerical approximation introduced by the vacuum as a region where the Euler equations are not valid due to the failure of the continuum assumption. The tracking algorithm is based on the exact or an approximate solution of the vacuum Riemann problem. This is the initial value problem with two constant states, one being the gas and the other the vacuum state, and a limit case of the usual Riemann problem. In this approach, the gas-vacuum boundary is sharply resolved within one mesh interval. For a test problem, the numerical results of gas flow into vacuum are presented which indicate that the gas vacuum boundary is captured very well.