Arbitrary Lagrangian-Eulerian methods for modelling high speed multi-material flows

Arbitrary Lagrangian Eulerian methods are well suited to modelling high speed compressible multimaterial flow problems in complex geometry. In this talk three stage ALE schemes will be considered, which are typically used for practical calculations of multimaterial flows. These three stages are: a Lagrangian stage, in which the solution and the computational mesh are updated; a rezoning stage, in which the nodes of the computational mesh are moved to more optimal positions; and a remapping stage, in which the Lagrangian solution is transferred to the rezoned mesh. This talk will give a brief overview of these methods [1] and then focuss on two topics in more detail; cell centred Lagrangian schemes and closure models for multimaterial cells.