Multidimensional Riemann Solvers and Higher Order Schemes with AMR for Computational Astrophysics

用于计算天体物理学的多维黎曼求解器和具有 AMR 的高阶方案

基本信息

批准号：
1009091
负责人：
Dinshaw Balsara
金额：
$ 36.27万
依托单位：
University of Notre Dame
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2010
资助国家：
美国
起止时间：
2010-09-15 至 2014-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1009091&HistoricalAwards=false
关键词：
Multidimensional Riemann Solvers Higher Order

项目摘要

Computation plays an increasingly important role in several fields of astrophysics, where theoretical work is now often driven by numerical results coming from hydrodynamic and magneto-hydrodynamic (MHD) codes. There remain several technical problems, a prime example of which is the need to include multi-dimensional flow effects when treating electric fields in divergence-free MHD codes. This project will build on recent advances in order to arrive at a genuinely three-dimensional Riemann solver for hydrodynamics and MHD and their relativistic variants. The work will also devise very low dissipation and large time-step versions of the multidimensional Riemann solvers. Integrating the resulting solvers with very efficient higher order algorithms for adaptive calculations will produce astrophysical adaptive mesh refinement codes with extremely high scalability to hundreds or thousands of processors. The result will be a new class of higher order schemes for simulating hyperbolic systems.Although astrophysical codes are widely used, they are often not very well understood: to help bridge this gap, Dr. Balsara is writing a pedagogical textbook, and some of the codes embodying techniques developed in the present project will be freely distributed to complement the textbook. Of course, these techniques are applicable to several exciting areas of astrophysics. Students and postdoctoral researchers involved in this study will receive well-organized interdisciplinary training through a coordinated educational plan.

计算在天体物理学的多个领域中发挥着越来越重要的作用，这些领域的理论工作现在通常由来自流体动力学和磁流体动力学 (MHD) 代码的数值结果驱动。仍然存在一些技术问题，其中一个主要的例子是在无散 MHD 代码中处理电场时需要包括多维流效应。该项目将建立在最新进展的基础上，以获得真正的三维黎曼求解器，用于流体动力学和 MHD 及其相对论变体。这项工作还将设计耗散极低、时间步长版本的多维黎曼求解器。将所得求解器与用于自适应计算的非常高效的高阶算法相集成，将产生天体物理自适应网格细化代码，该代码具有极高的可扩展性，可容纳数百或数千个处理器。结果将是用于模拟双曲系统的一类新的高阶方案。尽管天体物理学代码被广泛使用，但它们通常不是很好理解：为了帮助弥合这一差距，巴尔萨拉博士正在编写一本教学教科书，其中一些包含本项目开发的技术的代码将免费分发，以补充教科书。当然，这些技术适用于天体物理学的几个令人兴奋的领域。参与这项研究的学生和博士后研究人员将通过协调的教育计划接受组织良好的跨学科培训。