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Adaptive numerical algorithms in space weather modeling

机译：空间天气建模中的自适应数值算法

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Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different relevant physics in different domains. A multi-physics system can be modeled by a software framework comprising several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models.Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamic (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems.BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure.The framework and the adaptive algorithms enable physics-based space weather modeling and even short-term forecasting.
机译：太空天气描述了太阳地球系统中对人类健康和技术构成威胁的各种过程。空间天气预报的目标是提供减轻这些负面影响的机会。基于物理学的空间天气建模的特点是时空尺度不同，不同领域的相关物理学也不同。可以通过包含几个组件的软件框架对多物理场系统进行建模。每个组成部分对应一个物理领域，每个组成部分由一个或多个数值模型表示。公开可用的空间天气建模框架（SWMF）可以灵活高效地执行并分发分布在并行计算机上的多个组件。该框架还允许在各种模型中使用独立的时空离散化解决不同的时空尺度。该框架中计算上最昂贵的几个领域均由“块自适应树日风罗伊型上风方案”（BATS-R-美国）代码，可以解决各种形式的磁流体动力学（MHD）方程，包括霍尔，半相对论，多物种和多流体MHD，各向异性压力，辐射传输和热传导。在BATS-R-US中，通过在直角坐标系和广义坐标系中都采用块自适应网格，可以对不同的比例进行建模。最近，我们为BATS-R-US创建了一个新的核心：块自适应树库（BATL），它提供了用于在1、2或3维块自适应网格中创建，负载均衡和消息传递的通用工具包。我们描述了BATL的算法并展示了其针对各种问题的效率和缩放特性.BATS-R-US使用几种时间积分方案来解决多个时间尺度：显式时间步长具有固定或局部时间步长，部分稳态演化，点隐式，半隐式，显式/隐式和完全隐式数值方案。根据应用，我们发现不同的时间步进方法是最佳的。一些时间积分方案利用网格结构的基于块的粒度。框架和自适应算法可实现基于物理的空间天气建模，甚至是短期预报。

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