Simultaneous untangling and smoothing of moving grids

Abstract

In this paper a technique for simultaneous untangling and smoothing of meshes is presented. Itis based on an extension of an earlier mesh smoothing strategy developed by the authors and used to solve the computational mesh dynamics stage in fluid-structure interaction problems. In moving grid problems, mesh untangling is necessary when element inversion happens due to a moving domain boundary. The original smoothing strategy is defined in terms of the minimization of a functional associated with the mesh distortion using an indicator of the element geometric quality. This functional becomes discontinuous when an element has null volume, making impossible to obtain a valid mesh from an invalid one. To circumvent this drawback, the original functional is transformed in order to guarantee its continuity for the whole space of nodal coordinates, achieving the untangling technique. The regularization depends on one parameter, allowing the recovery of the original functional when this parameter tends to zero. This feature is very important because at first it is necessary to regularize the functional in order to make the mesh valid, but then, it is advisable to use the original functional to make the smoothing optimal. This technique is applied to several test cases, including 2D and 3D meshes with simplicial elements. An additional example shows how this technique may be used for mesh generation.