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

#### Abstract

Shock waves and contact discontinuities usually appear in compressible ﬂows, requiring a ﬁne mesh in order to achieve an acceptable accuracy of the numerical solution. The usage of a mesh adaptation strategy is convenient as uniform reﬁnement of the whole mesh becomes prohibitive in three-dimensional problems. An unsteady h-adaptive strategy for unstructured ﬁnite element meshes is introduced. The non-conformity of the reﬁned mesh and a bounded decrease in the geometrical quality of the elements are some features of the reﬁnement algorithm. A three-dimensional extension of the well known reﬁnement constraint for two-dimensional meshes is used to enforce a smooth size transition among neighbour elements with different levels of reﬁnement. A density-based gradient indicator is used to track discontinuities. The solution procedure is partially parallelized, i.e: the inviscid ﬂow equations are solved in parallel with a streamline upwind Petrov-Galerkin ﬁnite element formulation with shock capturing terms while the adaptation of the mesh is sequentially performed. Results are presented for a spherical blast wave driven by a point-like explosion with an initial pressure jump of 105 atmospheres. The adapted solution is compared to that computed on a ﬁxed mesh. Also, results provided by the theory of self-similar solutions are considered for the analysis. In this particular problem, adapting the mesh to the solution accounts for approximately 4% of the total simulation time and the reﬁnement algorithm scales almost linearly with the size of the problem.