Arbitrary Lagrangian Eulerian formulation for two-dimensional flows using dynamic meshes with edge swapping

The dynamic modification of the computational grid due to element displacement, deformation and edge swapping is described here in terms of suitably-defined continuous (in time) alterations of the geometry of the elements of the dual mesh. This new interpretation allows one to describe all mesh modifications within the arbitrary Lagrangian Eulerian framework, thus removing the need to interpolate the solution across computational meshes with different connectivity. The resulting scheme is by construction conservative and it is applied here to the solution of the Euler equations for compressible flows in two spatial dimensions. Preliminary two dimensional numerical simulations are presented to demonstrate the soundness of the approach. Numerical experiments show that this method allows for large time steps without causing element invalidation or tangling and at the same time guarantees high quality of the mesh elements without resorting to global re-meshing techniques, resulting in a very efficient solver for the analysis of e.g. fluid-structure interaction problems, even for those cases that require large mesh deformations or changes in the domain topology.