Robert Anderson, Noah Elliott, Richard Pember

Adaptive Mesh Refinement for Staggered Grid Arbitrary Lagrangian Eulerian Methods

A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian discretizations as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Interlevel transfer operators and hierarchy integration algorithms are developed first for a purely Lagrangian method, and then generalized to the ALE context. The resulting method is evaluated with respect to a number of design goals and priorities.

The method is then applied to a variety of test problems and quantitatively evaluated with respect to an AMR solution efficiency metric which weighs relative accuracy degradation against faster solution time, relative to a uniformly fine resolution solution for each problem. A number of adaption criteria are also considered and quantitatively evaluated with respect to this metric.