Multigrid methods applied to an explosion at a plane density interface

The astrophysical problem of a supernova explosion at the edge of a dense molecular cloud or a diffuse stellar wind bubble is simplified to that of a point explosion at a plane density interface separating two uniform media with density ratio a. This approximation gives rise to a self-similar flow which can be found by transforming the hydrodynamic equations to the similarity plane and looking for the steady solution there. A flux vector splitting scheme, together with the use of multigrid techniques provides us with a robust and efficient method of finding this steady solution. The high-resolution results so produced reveal the formation of a supersonic jet along the symmetry axis when the density ratio is large enough. (author)