Elements: ALE-AMR Framework and the PISALE Codebase

在现代高性能计算(HPC)平台上求解偏微分方程组(PDE)对于对国家利益具有重要意义的各种领域的研究和建模的持续成功至关重要。该项目将提供用于PDE建模的软件。它还将应用该代码来模拟夏威夷群岛复杂的地下水流动过程，这些岛屿的特点是高度不均匀的火山岩以及淡水和海水之间的动态相互作用。美国大约一半的人口居住在沿海地区，那里的地下水提供了大部分家庭、农业和工业用水。夏威夷几乎所有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地下咸水之上，这使得它非常容易受到人为活动和可能的海水和火山事件引发的咸水入侵的影响。对夏威夷的地下水资源进行适当的建模和管理以实现可持续利用是至关重要的。在HPC上用偏微分方程进行海岛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。该项目中的软件将既用于应用程序，又作为学生参与HPC的纽带。将编写与该项目有关的课程材料，并在大学一级的地下水建模课程中提供。在本项目中开发、分发和应用的PDE软件使用了先进数学技术的创新组合来求解偏微分方程组，包括动态调整网格的并行软件工具和特殊的拉格朗日流动方法，这些方法允许求解能够再现在海水监测点观测到的尖锐淡水-海水界面的方程。该软件特别适合于具有可以以守恒定律形式表述的方程的应用。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分量的能力。该软件基于ALE(任意拉格朗日欧拉方法)和AMR(自适应网格细化)的技术，以创建软件的公共可持续分支，称为Pisale for Pacific Island Structure-AMR With ALE。除了在夏威夷含水层的地下流动和运输应用外，该项目还将在需要在先进的HPC架构上高效解决PDE的各种领域提供合作研究的能力。该奖项由NSF高级数字基础设施办公室联合支持，该项目是由NSF地球科学局地球科学部门的水文科学计划联合支持的。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.