This paper is concerned with numerical solutions of 3-dimensional spherical flows. We consider the spherical flow arising from the expanding piston and preceded by a shock front. Godunov’s scheme and the modified Glimm scheme are applied to solve the compressible Euler equations. The shock wave can be tracked by use of the moving grid system. The wave patterns for both schemes are presented in comparison with the self-similar solutions and they have a good agreement. In particular, our works for different initial and boundary conditions demonstrate the asymptotic character of the self-similar solutions.

Euler equation, shock wave, self-similarity.