Numerical simulation of incompressible flows using adaptive unstructured meshes and the pseudo-compressibility hypothesis

The numerical simulation of incompressible viscous flows, using finite elements with automatic adaptive unstructured meshes and the pseudo-compressibility hypothesis, is presented in this work. Special emphasis is given to the automatic adaptive process of unstructured meshes with linear tetrahedral elements in order to get more accurate solutions at relatively low computational costs. The behaviour of the numerical solution is analyzed using error indicators to detect regions where some important physical phenomena occur. An adaptive scheme, consisting in a mesh refinement process followed by a nodal re-allocation technique, is applied to the regions in order to improve the quality of the numerical solution. The error indicators, the refinement and nodal re-allocation processes as well as the corresponding data structure (to manage the connectivity among the different entities of a mesh, such as elements, faces, edges and nodes) are described. Then, the formulation and application of a mesh adaptation strategy, which includes a refinement scheme, a mesh smoothing technique, very simple error indicators and an adaptation criterion based in statistical theory, integrated with an algorithm to simulate complex two and three dimensional incompressible viscous flows, are the main contributions of this work. Two numerical examples are presented and their results are compared with those obtained by other authors.