Transmission of a slowly moving shock across a nonconservative interface

Computational fluid dynamics using composite overlapping grids plays an imp ortant role in today's fluid mechanics with complex flows. The key point in the overlapping grid method is how to ensure conservation for shock waves. This was first studied by M. Berger under the framework of weak solutions for vanishing mesh size, leading to the well-known flux interpolation inter face condition (SIAM J. Numer. Anal. 24, 967(1987)), The present author use d the Rankine-Hugoniot relation to directly analyze the transmission of a s hock across the interface and showed that, for the scalar Burgers equation, a nonconservative treatment leads to correct transmission of shocks even f or finite mesh sizes if the interior difference scheme contains enough diss ipation, and that shock penetration trouble only occurs for very slowly mov ing shock waves (SLAM J. Sci. Comput. 20, 1850 (1999)). This is reconsidere d here for the system of Euler equations in gas dynamics. Numerical experim ents show that for weakly dissipative schemes, slowly moving shock waves fa il to transmit the nonconservative interface by producing finally a nonphys ical, two-shocked steady-state solution. By using the dynamics of a very sl owly moving shock, we will show that two-shocked steady-state solutions are avoided if the interior difference scheme is no less dissipative than the standard Roe scheme even though a nonconservative interface treatment is us ed. (C) 2001 Academic Press.