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We review the basic equations, numerical solution techniques, and new application areas of a novel multi-purpose computer code framework, PISALE, for the solution of complex Partial Differential Equation (PDE) systems on modern computing platforms. We describe how the code solves equations in the fluid approximation using a novel combination of ALE and AMR methods. Sample problems from areas of ground water flow, high-speed impacts, and X-ray Free Electron Laser (XFEL) experiments are given. 

The solution of partial differential equations (PDEs) on modern high performance computing (HPC) platforms is essential to the continued success of groundwater flow and transport modeling in Pacific islands where complex regional groundwater flow is governed by highly heterogeneous volcanic rocks and dynamic interaction between freshwater and seawater. For accurate simulations of complex groundwater flow processes in the Hawaiian islands, the PISALE (Pacific Island Structured-AMR with ALE) software has been developed to offer an innovative combination of advanced mathematical techniques such as arbitrary Lagrangian-Eulerian method (ALE) and Adaptive Mesh Refinement (AMR). The software uses parallel programming models to accelerate the time to solution and dynamically adapt the grids using AMR. This allows for the solution of equations that can reproduce the sharp freshwater-seawater interface in large-scale coast aquifers. In this work, we summarize our ongoing efforts to create a publicly available sustainable branch of the software focused on the groundwater problem. The island-scale numerical groundwater flow modeling will play an important role in predicting the sustainable yields and potential contaminant transport for the volcanic aquifer systems and planning groundwater resources management.