Noh's constant-velocity shock problem revisited (Q1374697)

This paper examines the solutions to Noh's shock tube problem in planar, cylindrical and spherical geometries. An implicit adaptive grid algorithm allows the generation of the complete solution for each of the three specified geometries. A detailed discussion is presented for each case and, in particular, the shock is followed over many reflections. In the planar case an analytic solution is derived and the numerical error in the physical quantities involved is found to be less than \(1\%\) on a 100 grid-point computational domain. In the case of converging geometries an approximate analytical solution is given, and the deviation between theoretical and numerical results is found to be less than \(10\%\).