Simultaneous untangling and smoothing of moving grids

In this work, a technique for simultaneous untangling and smoothing of meshes is presented. It is based on an extension of an earlier mesh smoothing strategy developed to solve the computational mesh dynamics stage in fluid-structure interation problems. In moving grid problems, mesh untangling is necessary when element inversion happens as a result of a moving domain boundary. The smoothing strategy, formerly published by the authors, is defined in terms of the minimization of a functional associated with the mesh distortion by using a geometric indicator of the element quality. This functional becomes discontinuous when an element has null volume, making it impossible to obtain a valid mesh from an invalid one. To circumvent this drawback, the functional proposed is transformed in order to guarantee its continuity for the whole space of nodal coordinates, thus achieving the untangling technique. This regularization depends on one parameter, making the recovery of the original functional possible as this parameter tends to 0. This feature is very important: consequently, it is necessary to regularize the functional in order to make the mesh valid; then, it is advisable to use the original functional to make the smoothing optimal. Finally, the simultaneous untangling and smoothing technique is applied to several test cases, including 2D and 3D meshes with simplicial elements. As an additional example, the application of this technique to a mesh generation case is presented. Copyright (C) 2008 John Wiley & Sons. Ltd.