Computational Methods for Astrophysical Flows

天体物理流的计算方法

• 批准号: 0711885
• 负责人: James Rossmanith
• 金额: $ 15万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-15 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0711885&HistoricalAwards=false
• 关键词: Computational; Methods; Astrophysical; Flows; Computational; Methods; Astrophysical; Flows

Astrophysical fluid dynamics is a branch of physics concerned with understanding the evolution of far-away objects such as black holes and neutron stars. In order to fully understand such objects, mathematical models must incorporate general relativistic, electromagnetic, and fluid dynamic effects. The resulting equations are a large, coupled, nonlinear system of partial differential equations, some of which are evolution equations, while others are constraint equations that result from various gauge freedoms. The PI's research will focus on developing high-order schemes on unstructured grids to solve various simplified versions of the full astrophysical fluid dynamic model. For example, one problem of great interest to astrophysicists is that of mass accretion onto black holes and the resulting formation of relativistic jets; this phenomenon can be treated in the test-fluid limit (i.e., background spacetime metric is fixed). Another important problem is the generation of gravitational waves (i.e., ripples in spacetime) from the collision of two massive black holes; this problem can be first looked at in the minimally coupled scalar field limit. The PI will make use of both discontinuous Galerkin and residual distribution scheme methodologies to construct accurate and efficient schemes. In particular, these methods will be combined with adaptive mesh refinement strategies. In order to do this efficiently, the PI will construct a posteriori error estimators that can be used to dynamically diagnose where large numerical errors are being made. The resulting set of numerical methods will be incorporated into a computer code that will be made freely available on the web.Although astrophysical objects such as black hole accretion disks, extragalactic jets, and supernovae are observable using various telescopes, direct experimentation is clearly not possible. On the other hand, mathematical models that attempt to explain the physics of these objects are necessarily complex and must include gravitational, electromagnetic, and fluid dynamic effects. Exact solutions to the resulting mathematical equations can only be constructed in very special cases. Therefore, the ability to understand astrophysical phenomena from a scientific viewpoint rests largely on the ability to run accurate and efficient computer simulations, which, in turn, rests on the quality of the computational methods that are used to carry out those simulations. The PI's research is focused on developing classes of high-order computational methods for solving the equations of astrophysical fluid dynamics. One aspect of this work will involve the construction of various error indicators that can be used to dynamically diagnose and correct the accuracy of a computation. Another aspect will be to develop a software package that will be made freely available on the web. The computational methods that result from this development will be applied to two distinct problems in astrophysics: (1) the formation of astrophysical jets from black hole accretion processes and (2) the dynamics of the interaction of two black holes and the resulting generation of gravitational waves.

天体物理流体动力学是物理学的一个分支，涉及了解远处的物体（例如黑洞和中子星）的演变。为了充分理解此类对象，数学模型必须结合一般的相对论，电磁和流体动态效应。所得的方程是一个大的，耦合的，非线性的偏微分方程的非线性系统，其中一些是进化方程，而其他方程是由各种规格自由产生的约束方程。 PI的研究将着重于开发关于非结构化网格的高级方案，以求解整个天体物理流体动态模型的各种简化版本。例如，天体物理学家引起了极大兴趣的一个问题是将大量积聚到黑洞上，以及由此导致的相对论喷气机的形成。该现象可以在测试流体极限（即固定背景时空度量）中进行处理。另一个重要的问题是两个巨大的黑洞的碰撞产生引力波（即时空的波纹）。可以首先在最小耦合的标量场限制中查看此问题。 PI将利用不连续的Galerkin和残留分布方案方法来构建准确有效的方案。特别是，这些方法将与自适应网状精炼策略相结合。 为了有效地执行此操作，PI将构建一个后验误差估计器，该估计器可用于动态诊断发生较大的数值错误。最终的数值方法将被合并到一个计算机代码中，该计算机代码将在网络上免费提供。尽管可以使用各种望远镜观察到天体物理对象，例如黑洞积聚磁盘，外层状喷气机和超新星，但直接实验显然是不可能的。另一方面，试图解释这些物体物理学的数学模型必然很复杂，必须包括引力，电磁和流体动态效应。最终的数学方程式的确切解决方案只能在非常特殊的情况下构建。因此，从科学角度来理解天体物理现象的能力在很大程度上取决于运行准确有效的计算机模拟的能力，这反过来又取决于用于执行这些模拟的计算方法的质量。 PI的研究重点是开发用于解决天体物理流体动力学方程的高级计算方法类别。这项工作的一个方面将涉及构建各种误差指标，这些指标可用于动态诊断和纠正计算的准确性。另一个方面是开发一个软件包，该软件包将在网络上自由使用。该发展产生的计算方法将应用于天体物理学中的两个不同问题：（1）从黑洞积聚过程中形成了天体物理喷射，以及（2）两个黑洞相互作用的动力学以及导致引力波的产生。