The underlying physical experiment consists of a tube filled with hydrogen and oxygen. Both react and build a detonation front, moving to the right. The mathematical model consists of the compressible Euler equations with reactive source terms. They are solved by a finite volume scheme on an unstructured grid. Next to the detonation front the grid is locally refined and the refinement zone is moving with the front. Different geometries (e.g. with obstacles inside) of the tube are considered.