An H-Adaptive Non-Conformal 3-D Unstructured Mesh Strategy for Unsteady Compressible Flows

Abstract

An h-adaptive unstructured mesh refinement strategy to solve unsteady problems by the finite element method is described. Key features of the strategy are the non-conformity and both a prescribed updating frecuency and a maximum level of refinement for the adapted meshes. The 1-irregular node refinement constraint is extended to tetrahedral meshes to ensure a smooth grading in the elements size.
A particular 1:8 partitioning sequence, which shows to keep bounded the quality decrease, is applied to tetrahedral elements. The type of element is not changed and no transition templates are used, therefore hanging nodes appear in the adapted mesh. The elements’ refinement algorithm is described in some detail. The adaptivity strategy is implemented in C++ code using both the STL (Standard Template Library) and Boost Multiarray(http://www.boost.org/) libraries for the managment of the data structure. This code is used to solve the Taylor-Sedov spherical blast wave problem on an unstructured mesh of
tetrahedra.