A three-dimensional torsional spring analogy method for unstructured dynamic meshes

We present a three-dimensional spring analogy method for updating the position of unstructured dynamic meshes that features torsional springs for controlling the arbitrary motion of the grid points. We show that these torsional springs can be designed to prohibit the interpenetration of neighboring tetrahedra, and therefore to provide the method of spring analogy with the robustness needed for enlarging its range of applications. We illustrate the proposed spring analogy method with the solution of three-dimensional flow problems with complex moving boundaries, and where the unstructured meshes undergo significant deformations. We highlight the advantages of this method with respect to robustness and mesh quality, and address its computational performance.