### An h-Adaptive Solution of the Spherical Blast Wave Problem

#### Abstract

Compressible ﬂow problems usually exhibit features in the ﬂow ﬁeld that need a very reﬁned mesh in order to achieve an acceptable accuracy in the numerical solution. Uniform reﬁnement of the whole mesh quickly becomes prohibitive in three dimensions. In these situations, the use of an adaptive technique shows advantageous. Here, a h-reﬁnement/coarsening strategy for unstructured ﬁnite element meshes is described and applied to solve the spherical blast wave problem driven by a point-like intense explosion. The resulting meshes are non-conformal. A 3-D reﬁnement constraint is introduced to enforce a smooth size distribution among neighbor elements in the mesh and a gradient error indicator based on the ﬂow variables is used to track discontinuities. It is shown that the adaption strategy allows to improve the accuracy and to reduce the spurious oscillations in the numerical solution, requiring just a small fraction of the overall computing time.