Extension of efficient, swept-integration-based conservative remapping method for meshes with changing connectivity

In numerical simulations of fluid flow, the choice of the computational mesh is crucial. Traditionally, there have been two viewpoints, utilizing the Lagrangian or the Eulerian framework, each with its own advantages and disadvantages. In a pioneering paper [1], Hirt et al. developed the formalism for a mesh whose motion could be determined as an independent degree of freedom, and showed that this general framework could be used to combine the best properties of Lagrangian and Eulerian methods. This class of methods has been termed Arbitrary Lagrangian–Eulerian or ALE. It is most usual to separate the ALE algorithm into three individual phases. These are the following: (1) a Lagrangian phase, in which the solution and mesh are updated, (2) a rezoning phase, in which the nodes of the computational mesh are moved to a more optimal position, and (3) a remapping phase, in which the Lagrangian solution is interpolated onto the rezoned mesh. We are interested in the development of staggered ALE methods for meshes whose connectivity may