Numerical simulation of the viscous shock tube problem by using a high resolution monotonicity-preserving scheme

This work deals with the flow generated in a shock tube after the shock wave has reflected at the end wall. For a viscous fluid, a complex unsteady interaction takes place between the incident boundary layer and reflected shock wave. The numerical simulation of this complex flow requires both robust and accurate numerical schemes. In this work, we rely on the one-step high-order scheme recently proposed by Daru and Tenaud [Daru V, Tenaud C. High order one-step monotonicity preserving schemes for unsteady flow calculations. J Comput Phys 2004;193:563–94]. With this scheme, converged results are obtained for Reynolds numbers in the range 200–1000. The interaction mechanisms are carefully analyzed as well as the flow dynamics.