Elements: ALE-AMR Framework and the PISALE Codebase

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The solution of partial differential equations (PDEs) on modern high performance computing (HPC) platforms is essential to the continued success of research and modeling for a wide variety of areas of importance to the national interest. This project will make available software for modeling with PDEs. It will also apply the code for simulations of complex groundwater flow processes in Hawaiian islands characterized by highly heterogeneous volcanic rocks and dynamic interaction between freshwater and seawater. Roughly half the population in the US lives near coastal areas where groundwater supplies much of the domestic, agricultural, and industrial water supply. Almost all of Hawaii’s domestic water use is pumped from volcanic aquifer systems since the islands are completely surrounded by the Pacific Ocean. In Hawaii’s groundwater resources, freshwater accumulates on top of the denser underlying saltwater, making it highly susceptible to anthropogenic activities and saltwater intrusion induced by possible sea water and volcanic events. It is essential that Hawaii’s groundwater resources are properly modeled and managed for sustainable use. Island-scale numerical groundwater flow modeling with PDEs on HPC will play an important role in predicting the sustainable yields for the volcanic aquifer systems and planning groundwater resources management. The software in this project will be used both for applications and as a nexus for student involvement in HPC. Curriculum material associated with the project will be developed and offered at university level groundwater modeling classes. The PDE software developed, distributed, and applied in this project uses an innovative combination of advanced mathematical techniques for the solution of PDEs including parallel software tools to dynamically adapt the grids and special Lagrangian-flow methods that allow for solution of equations that can reproduce the sharp freshwater-seawater interface observed in sea water monitoring locations. The software is particularly appropriate for applications with equations that can be couched in a conservation law form. Source terms of these applications can be included using complex numerical techniques including the ability to handle anisotropic tensors components.The software is based on techniques of ALE (Arbitrary Lagrangian Eulerian Methods) with AMR (Adaptive Mesh Refinement) to create a publicly available sustainable branch of the software known as PISALE for Pacific Island Structured-amr with ALE. In addition to the subsurface flow and transport application in Hawaiian aquifers, the project will provide capability for collaborative research in a variety of fields that require efficient solution of PDEs on advanced HPC architectures.This award by the NSF Office of Advanced Cyberinfrastructure is jointly supported by the Hydrologic Sciences Program, part of the Division of Earth Sciences, within the NSF Directorate of Geosciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.