A Mesh Adaption Method by Node Re-Allocation Using an Edge-Based Error Measure

Abstract

A mesh adaptation technique implemented in an algorithm to simulate compressible flows characterized by the presence of strong shocks, using the finite element method (FEM), is presented in this work. The initial mesh is continuously adapted during the solution process using a node movement technique, keeping as much as possible mesh smoothness and local orthogonality with an unconstrained optimization method. The error is estimated as a function of the Hessian tensor, containing second derivatives of the specific mass, and a Riemann metric projected on the element edges is obtained in order to determine node movements. Time and spatial discretization of the governing equations are carried out using an explicit Taylor-Galerkin scheme and an isoparametric hexahedrical element with eight nodes. An Arbitrary Lagrangean Eulerian (ALE) description is used to take into account mesh movement. Finally, some two-dimensional examples involving transonic and supersonic flows are presented to validate the algorithm.