A semi-torsional spring analogy model for updating unstructured meshes in 3D moving domains

Here, we present a semi-torsional spring analogy model based on a consistent definition of the edge stiffness that avoids mis-shaped elements. The model is applicable to both 2D and 3D fully unstructured meshes, and includes a computationally efficient means of incorporating geometric information about element shape so as to allow element deformation while penalizing formation of mis-shaped elements, with little restriction on the magnitude of mesh deformation. Extensive numerical testing in 2D and 3D showed that the algorithm preserves mesh quality even under severe deformations. We conclude that the semi-torsional technique presented here is an improvement over existing spring-based mesh updating schemes.