Focusing of noncircular self-similar shock waves.
We study the focusing of noncircular shock waves in a perfect gas. We construct an explicit self-similar solution by combining three convergent plane waves with regular shock reflections between them. We then show, with a numerical Riemann solver, that there are initial conditions with smooth shocks whose intermediate asymptotic stage is described by the exact solution. Unlike the focusing of circular shocks, our self-similar shocks have bounded energy density.
Betelu
S I
SI
Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, Minneapolis, Minnesota 55455, USA.
Aronson
D G
DG