一阶粘性相对论流体力学守恒有限体积格式
Conservative finite volume scheme for first-order viscous relativistic hydrodynamics
摘要：
我们提出了第一个保守的有限体积数值格式的因果关系，稳定的相对论性纳维-斯托克斯方程开发的Bemfica，Disconzi，Noronha，和Kovtun（BDNK）。BDNK理论是最近出现的一种很有前途的方法，它将熵产生效应（粘性、热传导）纳入相对论性流体模型，似乎是成功用于模拟夸克-胶子等离子体的所谓穆勒-以色列-斯图尔特（MIS）理论的可能替代方案。两者之间的主要区别在于偏微分方程系统的结构：BDNK理论只有一组守恒律，而MIS理论还包括一组耗散自由度的演化方程。在这方面，BDNK偏微分方程的结构更简单，可以对稳定性、因果关系和双曲性进行严格的证明，这在MIS中是不可能的。为了利用这些优势，我们提出了第一个完全保守的多维流体求解器的BDNK方程适合物理应用。该方案包括一个通量守恒的离散化，非振荡重建，和一个中心迎风数值通量，并顺利过渡到一个高分辨率的激波捕捉完美的流体求解器在无粘限制。我们在一系列共形流体的平坦时空测试中评估了我们的新方法的鲁棒性，并与Pandya & Pretorius（2021）以前的方法进行了详细的比较。
英文摘要：
We present the first conservative finite volume numerical scheme for the causal, stable relativistic Navier-Stokes equations developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). BDNK theory has arisen very recently as a promising means of incorporating entropy-generating effects (viscosity, heat conduction) into relativistic fluid models, appearing as a possible alternative to the so-called Müller-Israel-Stewart (MIS) theory successfully used to model quark-gluon plasma. The major difference between the two lies in the structure of the system of PDEs: BDNK theory only has a set of conservation laws, whereas MIS also includes a set of evolution equations for its dissipative degrees of freedom. The simpler structure of the BDNK PDEs in this respect allows for rigorous proofs of stability, causality, and hyperbolicity in full generality which have as yet been impossible for MIS. To capitalize on these advantages, we present the first fully conservative multi-dimensional fluid solver for the BDNK equations suitable for physical applications. The scheme includes a flux-conservative discretization, non-oscillatory reconstruction, and a central-upwind numerical flux, and is designed to smoothly transition to a high-resolution shock-capturing perfect fluid solver in the inviscid limit. We assess the robustness of our new method in a series of flat-spacetime tests for a conformal fluid, and provide a detailed comparison with previous approaches of Pandya & Pretorius (2021).
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