Adaptive Re nement of Unstructured Finite Element Meshes for Compressible Flow

Abstract

It is well known that sudden changes in the solution produced by shock waves and contact discontinuities often appear in compressible flow problems. These features of the flow field require very small size finite elements to achieve an accurate solution. However, homogeneous refinement of the whole mesh quickly becomes prohibitive for three dimensional meshes due to computational cost issues. In these situations, the use of adaptive mesh refinement strategies shows advantageous. An h-adaptive unstructured mesh refinement strategy to solve both steady and unsteady compressible flow problems by the finite element method is used in this work. The adaption algorithm is briefly introduced. The main features of the adapted meshes are the presence of hanging nodes and the controlled geometrical quality of its elements. Refinement constraints are enforced to guarantee a smooth size distribution amongst neighbour elements and a posteriori error indicators based on the gradient of the flow variables are used to track discontinuities through the flow field. The algorithm is implemented in the C++ programming language together with the STL and Boost libraries. The mesh adaption code is coupled to an SUPGFEM flow solver which is run in parallel on a cluster of workstations. The spherical blast wave problem known as the Taylor-Sedov problem is solved with this code and the flow field is compared to that provided by the theory.