Adaptive Anisotropic Mesh Technique For Coupled Problems: Application To Welding Simulation

A major problem arising in finite element analysis of coupled problems, such as welding for instance, is the control of the mesh, that is an appropriate mastering of the spatial discretization to get accurate results in a minimum computer time. The present anisotropic adaptation procedure is controlled by a directional error estimator based on local interpolation error and recovery of the second derivatives of different fields involved in the finite element calculation. Error indicators are derived to define an anisotropic mesh metric field, which is an input of the pre existing 3D remeshing procedure. The mesh metric consists of a combination of several metrics, each corresponding to the error estimation associated with a selected field of the solution produced (temperature, phase fraction, stress component). Mesh modifications are used to anisotropically and continuously adapt the mesh. We demonstrate the efficiency of the method by applying it to a coupled thermal-mechanical-metallurgical simulation of arc welding. We demonstrate that the use of an anisotropic adaptive finite element method can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with isotropic meshes.