A minimal element distortion strategy for computational mesh dynamics

Mesh motion strategy is one of the key points in many fluid–structure interaction (FSI) problems. Due to the increasing application of FSI to solve the current challenging engineering problems, this topic has become of great interest. There are several different strategies to solve this problem, some of them use a discrete and lumped spring–mass system to propagate the boundary motion into the volume mesh, and many others use an elastostatic problem to deform the mesh. In all these strategies there is always risk of producing an invalid mesh, i.e. a mesh with some elements inverted. Normally this condition is irreversible and once an invalid mesh is obtained it is difficult to continue. In this paper the mesh motion strategy is defined as an optimization problem. By its definition this strategy can be classified as a particular case of an elastostatic problem where the material constitutive law is defined in terms of the minimization of certain energy functional that takes into account the degree of element distortion. Some advantages of this strategy are its natural tendency to high quality meshes, its robustness and its straightforward extension to 3D problems. Several examples included in this paper show these capabilities. Even though this strategy seems to be very robust it is not able to recover a valid mesh starting from an invalid one. This improvement is left for future work. Copyright q 2006 John Wiley & Sons, Ltd