面向数值相对论应用的人工粘性间断伽辽金方法
A discontinuous Galerkin method with artificial viscosity geared toward numerical relativity applications
- Florida Atlantic University（佛罗里达大西洋大学）
- CENTRA, Departamento de Física, Instituto Superior Técnico IST, Universidade de Lisboa UL（里斯本大学高等技术学院物理系CENTRA研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种带人工粘性的局部间断伽辽金方法，通过平滑度指示器仅在非光滑单元添加粘性，成功处理激波并首次在广义相对论流体动力学中演化单个中子星。
AI中文摘要：
人工粘性可用于处理激波以及其他不连续性，例如物质中可能出现的恒星表面。我们详细解释了如何使用局部间断伽辽金方法，在双曲演化方程中加入人工粘性项。这些人工项乘以一个粘性系数，该粘性系数仅在新开发的平滑度指示器标记为非光滑的单元中非零。我们的人工粘性方法在几个简单的激波测试案例中表现良好，例如Burgers方程和爆炸波测试。我们还首次能够在完全广义相对论流体动力学中演化单个中子星。为实现这一目标，我们对动量密度使用了与其余物质变量不同的粘性系数。
英文摘要：
Artificial viscosity can be used to deal with shocks and other discontinuities such as star surfaces, that can arise in matter. We explain in detail how a local discontinuous Galerkin method can be used to add artificial viscosity terms to hyperbolic evolution equations. These artificial terms are multiplied by a viscosity that is non-zero only in elements that are flagged as non-smooth by a newly developed smoothness indicator. Our artificial viscosity method works well in several simple shock test cases such as with Burgers' equation and blast wave tests. For the first time, we are also able to evolve single neutron star in full general relativistic hydrodynamics. To achieve this, we use different viscosities for the momentum density than for the rest of the matter variables.
