CDS&E: Collaborative: A Higher Order PDE Toolkit for Computational Mathematics and Astrophysical Turbulence

CDS

• 批准号: 1622457
• 负责人: Dinshaw Balsara
• 金额: $ 10万
• 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: 2016
• 资助国家: 美国
• 起止时间: 2016-09-15 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1622457&HistoricalAwards=false
• 关键词: CDS&E; Collaborative; Higher; Order; PDE

Our science and technology-driven society is immensely dependent on robust, reliable and highly accurate simulations of various natural phenomena. The scope of such natural phenomena is vast. In this proposal, the PIs take the task of generating software that can robustly, reliably and with high accuracy simulate phenomena that have to do with the propagation of wave-like motions. Such computational codes are very useful in simulating problems in applied and computational mathematics as well as computational astrophysics. The proposed effort seeks to develop a common software substrate for both those communities. The software is based on advanced computational algorithms and is intended to work very efficiently on modern generations of supercomputers that have been funded by the National Science Foundation. To solve the common problem faced by both communities the PIs develop a toolkit for higher order partial differential equation (PDE) methods. The proposed computational toolkit mainly includes two components. The first one is a multidimensional Riemann solver software that can work with some PDE systems. The second one is Discontinuous Galerkin (DG) schemes for some involution-constrained systems of hyperbolic PDEs such as Euler and magnetohydrodynamics (MHD) flows.

我们的科学技术驱动的社会极大地依赖于对各种自然现象的稳健、可靠和高精度的模拟。这种自然现象的范围是巨大的。在该提案中，PI 承担了生成软件的任务，该软件可以稳健、可靠且高精度地模拟与波状运动传播有关的现象。这种计算代码对于模拟应用和计算数学以及计算天体物理学中的问题非常有用。 拟议的工作旨在为这两个社区开发一个通用的软件基础。该软件基于先进的计算算法，旨在在美国国家科学基金会资助的现代超级计算机上非常高效地工作。为了解决两个社区面临的共同问题，PI 开发了一个用于高阶偏微分方程 (PDE) 方法的工具包。所提出的计算工具包主要包括两个组件。第一个是多维黎曼求解器软件，可以与某些偏微分方程系统一起使用。第二个是不连续伽辽金 (DG) 方案，适用于一些双曲偏微分方程的对合约束系统，例如欧拉流和磁流体动力学 (MHD) 流。

项目成果

Von Neumann stability analysis of globally divergence-free RKDG schemes for the induction equation using multidimensional Riemann solvers

• DOI: 10.1016/j.jcp.2017.01.056
• 发表时间: 2017-05-01
• 期刊: JOURNAL OF COMPUTATIONAL PHYSICS
• 影响因子: 4.1
• 作者: Balsara, Dinshaw S.;Kaeppeli, Roger
• 通讯作者: Kaeppeli, Roger

Computational electrodynamics in material media with constraint-preservation, multidimensional Riemann solvers and sub-cell resolution – Part II, higher order FVTD schemes

具有约束保持、多维黎曼求解器和子单元分辨率的材料介质中的计算电动力学 - 第二部分，高阶 FVTD 方案

• DOI: 10.1016/j.jcp.2017.10.013
• 发表时间: 2018
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Balsara, Dinshaw S.;Garain, Sudip;Taflove, Allen;Montecinos, Gino
• 通讯作者: Montecinos, Gino

Higher-order accurate space-time schemes for computational astrophysics—Part I: finite volume methods

• DOI: 10.1007/s41115-017-0002-8
• 发表时间: 2017-03
• 期刊: Living Reviews in Computational Astrophysics
• 作者: D. Balsara