Arbitrary Lagrangian Eulerian remap treatments consistent with staggered compatible total energy conserving Lagrangian methods

We describe new methods of computing post-remap nodal and subzonal masses in Arbitrary Lagrangian Eulerian (ALE) calculations employing the staggered energy conserving Lagrangian hydrodynamics method of Caramana et al. (1998) [12]. An important feature of this Lagrangian algorithm is the distribution of the masses to subzonal corners within each zone, which is then used to difference the momentum and energy equations such that both linear momentum and total energy are conserved. Such algorithms present challenges when employed as part of an ALE application, however, as these subzonal masses must be treated consistently through the remap phase. In this work we develop new ideas to compute the post-remap corner masses and associated mass fluxes between the nodal control volumes, such that the new corner masses (and therefore zonal and nodal masses) are consistently defined and conservation of linear momentum is ensured through the ALE step. We demonstrate applications of these ideas on examples including pure remapping and full ALE test cases.