National Science Foundation
07/2020 – 06/2023
Alice Koniges, and Jonghyun Lee
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 provide access to software for modeling with PDEs and also apply the code for simulations of complex groundwater flow processes in the Hawaiian islands characterized by highly heterogeneous volcanic rocks and dynamic interaction between freshwater and seawater. 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 the solution of equations that can reproduce the sharp freshwater-seawater interface observed in sea water monitoring locations. The software is based on the techniques of Arbitrary Lagrangian Eulerian Methods (ALE) with Adaptive Mesh Refinement (AMR) to create a publicly available sustainable branch of the software known as PISALE (for Pacific Island Structured-AMR with ALE). 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.