论文标题
一阶粘性相对论流体动力学的保守有限体积方案
Conservative finite volume scheme for first-order viscous relativistic hydrodynamics
论文作者
论文摘要
我们介绍了由Bemfica，Disconzi，Noronha和Kovtun（BDNK）开发的因果关系稳定的Navier-Stokes方程的第一个保守有限数值方案。 BDNK理论最近是一种有希望的方法，将熵产生效应（粘度，热传导）纳入相对论流体模型，似乎是成功用于模拟Quark-Gluon Plasma模型的所谓Müller-Israel-Stewart（MIS）理论的可能替代方法。两者之间的主要区别在于PDES系统的结构：BDNK理论仅具有一组保护定律，而MIS还包括一组耗散自由度的进化方程。在这方面，BDNK PDE的更简单结构可以使稳定性，因果关系和过于双曲线的严格证明，这对于MIS而言尚不不能。为了利用这些优势，我们提出了适合物理应用的BDNK方程的第一个完全保守的多维流体求解器。该方案包括通量保守的离散化，非振荡重建和中央风通量，并旨在平稳过渡到Inviscid极限处的高分辨率冲击捕获完美的流体求解器。我们在一系列平面测试中评估了新方法的鲁棒性，以进行保形流体，并与Pandya＆Pretorius（2021）的先前方法进行了详细的比较。
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).
