The Sedov Blast Wave as a Radial Piston Verification Test

The Sedov blast wave is of great utility as a verification problem for hydrodynamic methods. The typical implementation uses an energized cell of finite dimensions to represent the energy point source. This approximation can be avoided by directly finding the effects of the energy source as a boundary condition (BC). The proposed method transforms the Sedov problem into an outward moving radial piston problem with a time-varying velocity. A portion of the mesh adjacent to the origin is removed and the boundaries of this hole are forced with the velocities from the Sedov solution. This verification test is implemented on two types of meshes, and convergence is shown. The results from the typical initial condition (IC) method and the new BC method are compared.