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. Figure 20. Deformed mesh.Non-slip boundary conditions were imposed at the channel walls. The mesh used has 12K triangular elements and 6.7K nodes. Maximum channel blockage: 38%.In the original problem the maximum blockage of the channel is defined as 38% [33]. Figures 23-25 show the pressure, the velocity vector field and the velocity magnitude, respectively, at t * = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0. In these figures only the domain region downstream to the indentation is included due to the fact that the

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 interaction 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.