Some new developments of the singularity-separating difference method

The singularity-separating difference method is applied to the problem of calculating the problem of interaction between three-dimensional discontinuities in unsteady supersonic multimaterial flow. At the beginning of the flow, there are a shock and a contact discontinuity with different materials on its two sides. The shock then intersects the contact discontinuity, and a shock (or centered wave) is reflected. There are finally two shocks, or a shock and a centered wave, and a contact discontinuity in the flow field. Shocks, contact discontinuities, and boundaries of centered waves are taken as internal boundaries, and the problem is solved usign a second-order mixed scheme for initial-boundary-value problems. For comparison with other methods, calculations were carried out using the L-W scheme for an unsteady flow with a shock, a contact discontinuity, and a centered wave.