熵限流体力学:相对论流体力学的新方法

Federico Guercilena, David Radice, Luciano Rezzolla
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引用次数: 13

摘要

我们提出了熵限流体力学(ELH):一种计算守恒形式双曲方程离散过程中产生的数值通量的新方法。ELH是基于一阶Lax-Friedrichs方法与未滤波高阶格式的杂交。该方案的低阶部分的激活是由由Guermond等人(J.?Comput)提出的人工黏度方法激发的局部生成熵的度量来驱动的。物理学报,2011,31 (11):448 -4267,doi:10.1016/j.jcp.2010.11.043。在这里,我们在高阶有限差分方法和广义相对论流体力学方程的背景下提出ELH。我们研究了ELH在广义相对论中涉及孤立、旋转和非旋转中子星的一系列经典天体物理测试中的性能,并包括引力坍缩到黑洞的情况。我们给出了ELH与J. Comput中的五阶保持单调性方法MP5 (Suresh and Huynh)的详细比较。物理学报,36(1):83-99,1997,doi:10.1006/jcph.1997.5745),是目前在数值相对论模拟中最常用的高阶格式之一。我们发现,在这里研究的许多情况下,ELH以计算成本的一小部分(高达\({\sim}50\%\)加速)达到了与传统方法相当的精度,并且在许多情况下比传统方法更好。考虑到它的准确性和实现的简单性,ELH是一个很有前途的框架,可以用于开发新的特殊相对论和广义相对论流体力学代码,并很好地适应大规模并行超级计算机。
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Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics

We present entropy-limited hydrodynamics (ELH): a new approach for the computation of numerical fluxes arising in the discretization of hyperbolic equations in conservation form. ELH is based on the hybridisation of an unfiltered high-order scheme with the first-order Lax-Friedrichs method. The activation of the low-order part of the scheme is driven by a measure of the locally generated entropy inspired by the artificial-viscosity method proposed by Guermond et al. (J.?Comput. Phys. 230(11):4248-4267, 2011, doi:10.1016/j.jcp.2010.11.043). Here, we present ELH in the context of high-order finite-differencing methods and of the equations of general-relativistic hydrodynamics. We study the performance of ELH in a series of classical astrophysical tests in general relativity involving isolated, rotating and nonrotating neutron stars, and including a case of gravitational collapse to black hole. We present a detailed comparison of ELH with the fifth-order monotonicity preserving method MP5 (Suresh and Huynh in J.?Comput. Phys. 136(1):83-99, 1997, doi:10.1006/jcph.1997.5745), one of the most common high-order schemes currently employed in numerical-relativity simulations. We find that ELH achieves comparable and, in many of the cases studied here, better accuracy than more traditional methods at a fraction of the computational cost (up to \({\sim}50\%\) speedup). Given its accuracy and its simplicity of implementation, ELH is a promising framework for the development of new special- and general-relativistic hydrodynamics codes well adapted for massively parallel supercomputers.

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