Elements: ALE-AMR Framework and the PISALE Codebase

现代高性能计算（HPC）平台上的偏微分方程（PDE）的解决方案对于国家利益重要的各种领域的研究和建模的持续成功至关重要。该项目将提供偏微分方程建模软件。它还将应用该代码模拟夏威夷群岛复杂的地下水流动过程，这些岛屿的特点是火山岩高度不均匀，淡水和海水之间存在动态相互作用。美国大约有一半的人口居住在沿海地区，那里的地下水供应了大部分的家庭，农业和工业用水。 几乎所有的夏威夷的生活用水都是从火山含水层系统中抽取的，因为这些岛屿完全被太平洋包围。在夏威夷的地下水资源中，淡水积聚在密度较高的底层盐水之上，使其极易受到人为活动和可能的海水和火山事件引起的盐水入侵的影响。夏威夷的地下水资源必须得到适当的模拟和管理，以实现可持续利用。基于HPC的偏微分方程岛屿尺度地下水流数值模拟将在预测火山含水层系统的可持续开采量和规划地下水资源管理方面发挥重要作用。该项目中的软件将用于应用程序，并作为学生参与HPC的纽带。与该项目相关的课程材料将在大学水平的地下水建模课程中开发和提供。PDE软件的开发，分发，并在这个项目中应用，使用先进的数学技术的解决方案的PDE包括并行软件工具，以动态地适应网格和特殊的拉格朗日流方法，允许方程的解决方案，可以重现尖锐的淡水海水界面观察到的海水监测位置。该软件特别适用于方程可以表达在守恒律形式的应用程序。这些应用程序的源项可以使用复杂的数值技术，包括处理各向异性张量组件的能力。该软件是基于ALE（任意拉格朗日欧拉方法）与AMR（自适应网格细化）的技术，以创建一个公开可用的可持续的分支的软件被称为PISALE的太平洋岛屿结构-AMR与ALE。 除了夏威夷含水层的地下水流和运输应用外，该项目还将为需要在高级HPC架构上高效解决PDE的各种领域的合作研究提供能力。NSF高级网络基础设施办公室的这一奖项由水文科学计划共同支持，该计划是地球科学部的一部分，该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.