SI2-SSE: Development and Implementation of Software Elements using State-of-the-Art Computational Methodology to Advance Modeling Heterogeneities and Mixing in Earth's Mantle

SI2-SSE：使用最先进的计算方法开发和实施软件元素，以推进地幔异质性和混合的建模

• 批准号: 1440811
• 负责人: Elbridge Puckett
• 金额: $ 48.71万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1440811&HistoricalAwards=false
• 关键词: SI2; SSE; Development; Implementation; Software

This project involves the development and implementation of scientific software elements (SSEs), based on modern, high-resolution numerical methods for modeling steep gradients and sharp interfaces of material properties in viscous fluids in the presence of thermal convection. The goal of this project is to address a compelling need in geodynamics, in which continuum mechanics is applied to the study of geophysical processes, such as convection in the Earth?s mantle. A primary tool of geodynamics research is computational models of the flow of the extremely viscous interior of the Earth over hundreds of millions to billions of years. A long-standing challenge for these models is the need to accurately model sharp interfaces in temperature, viscosity, and other properties. These arise when, for example, modeling subduction (in which a cold tectonic plate plunges into the hot interior) or rising plumes (in which a hot boundary layer instability rises through the mantle and encounters the cold boundary layer of the tectonic plates). The project will foster interdisciplinary communication and the application of state-of-the-art applied and computational mathematics to fundamental problems in geophysics. It involves early-career mathematical scientists in the application of state-of-the-art numerical algorithms to geodynamics and, in particular, will provide an opportunity to increase the participation of women in mathematics and geodynamics research.This project involves the design and implementation of state-of-the-art SSEs for computing the evolution of significant processes in the Earth's mantle in which an essential feature of the problem is the presence of one or more moving boundaries, interfaces, or steep gradients in temperature, composition, or viscosity. The SSEs will address two critical issues that currently limit modern mantle convection simulations. All computational models of mantle convection currently in use produce significant overshoot and undershoot in the neighborhood of sharp gradients in temperature and viscosity. The cause of these overshoots and undershoots is a numerical artifact, which is well-known and well-understood in other fields, such as the computational shock physics community. Over the past thirty years researchers in computational shock physics have developed a variety of high-order accurate, monotone numerical methods, which preserve the physically correct maximum and minimum values of the computed quantities, while producing a high-order accurate numerical approximation of these quantities. Another compelling need in computational geodynamics is the ability to track discontinuous jumps in quantities such as material composition. Here high-order accurate interface tracking algorithms are required, since these fields undergo large-scale deformation, yet quantities such as the viscosity must be accurately approximated at the interface between two materials.

该项目涉及科学软件元素 (SSE) 的开发和实施，该元素基于现代高分辨率数值方法，用于对存在热对流的情况下粘性流体中材料特性的陡峭梯度和尖锐界面进行建模。该项目的目标是满足地球动力学的迫切需求，其中连续介质力学应用于地球物理过程的研究，例如地幔中的对流。地球动力学研究的主要工具是地球内部极其粘稠的内部数亿至数十亿年流动的计算模型。这些模型面临的长期挑战是需要对温度、粘度和其他属性的尖锐界面进行精确建模。例如，当模拟俯冲（其中冷的构造板块陷入热的内部）或上升的羽流（其中热边界层不稳定性通过地幔上升并遇到构造板块的冷边界层）时，就会出现这种情况。该项目将促进跨学科交流以及最先进的应用和计算数学在地球物理学基本问题上的应用。它涉及早期职业数学科学家将最先进的数值算法应用于地球动力学，特别是，将为增加女性参与数学和地球动力学研究提供机会。该项目涉及设计和实施最先进的 SSE，用于计算地幔中重要过程的演化，其中问题的基本特征是存在一个或多个移动边界、界面或温度、成分或粘度的陡峭梯度。 SSE 将解决目前限制现代地幔对流模拟的两个关键问题。目前使用的所有地幔对流计算模型都会在温度和粘度的急剧梯度附近产生显着的过冲和下冲。这些过冲和下冲的原因是数值伪影，这在其他领域（例如计算冲击物理界）是众所周知且易于理解的。在过去的三十年里，计算冲击物理学的研究人员开发了各种高阶精确、单调数值方法，这些方法保留了计算量的物理正确的最大值和最小值，同时产生这些量的高阶精确数值近似。计算地球动力学的另一个迫切需求是跟踪材料成分等数量的不连续跳跃的能力。这里需要高阶精确的界面跟踪算法，因为这些场经历大规模变形，但必须在两种材料之间的界面处精确地近似诸如粘度之类的量。