针对固定时空中对称约化广义相对论流体动力学的熵稳定且物理约束保持的间断伽辽金谱元方法
Entropy-Stable and Physical-Constraint-Preserving DGSEM for Symmetry-Reduced General-Relativistic Hydrodynamics on Stationary Spacetimes
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中文总结 AI 辅助
该研究开发了一种熵稳定且物理约束保持的DGSEM，结合多种技术实现了固定时空中对称约化广义相对论流体动力学的高精度、鲁棒数值模拟，经多类相对论流动算例验证了其性能。
中文摘要 AI 辅助
我们针对固定时空中对称约化广义相对论流体动力学，开发了一种熵稳定且物理约束保持的间断伽辽金谱元方法（DGSEM）。通过使用局部正交变换，流体变量被表示为相对论流体动力学代数和容许集不依赖于空间度量的形式，而时空几何则通过固定系数引入。这种分离使得熵守恒的狭义相对论通量可与几何源项的相容离散化相结合。在仿射张量积网格上，所得DGSEM是守恒的且满足半离散熵不等式，同时变换后的变量为物理约束保持提供了凸框架。为实现实用的稳定化，我们使用仅依赖几何的因果速度，其对经典局部Lax-Friedrichs熵耗散和物理约束保持的Lax-Friedrichs分裂均是充分的。全离散方法将该稳定化与SSP Runge-Kutta时间步进、振荡消除以及守恒的局部正交状态缩放相结合。数值实验涵盖光滑和强激波的狭义相对论流动、轴对称喷流、固定Michel吸积、Schwarzschild Bondi-Hoyle流动以及四个Kerr吸积案例。结果表明，该方法在光滑区域具有设计的高阶精度，且在弯曲固定背景下的苛刻相对论流动中表现出鲁棒性能。
英文摘要
We develop an entropy-stable and physical-constraint-preserving discontinuous Galerkin spectral element method for symmetry-reduced general-relativistic hydrodynamics on prescribed stationary spacetimes. Using a local orthonormal transformation, the fluid variables are expressed in a form for which the relativistic hydrodynamic algebra and the admissible set are independent of the spatial metric, while the spacetime geometry enters through stationary coefficients. This separation allows entropy-conservative special-relativistic fluxes to be combined with a compatible discretization of the geometric source terms. On affine tensor-product meshes, the resulting DGSEM is conservative and satisfies a semidiscrete entropy inequality, while the transformed variables provide a convex framework for physical-constraint preservation. For practical stabilization, we use a geometry-only causal speed that is sufficient for both classical local Lax--Friedrichs entropy dissipation and the physical-constraint-preserving Lax--Friedrichs splitting. The fully discrete method combines this stabilization with SSP Runge--Kutta time stepping, oscillation elimination, and conservative local-orthonormal-state scaling. Numerical experiments cover smooth and strongly shocked special-relativistic flows, an axisymmetric jet, stationary Michel accretion, Schwarzschild Bondi--Hoyle flow, and four Kerr accretion cases. The results demonstrate the designed high-order accuracy in smooth regimes and robust performance for demanding relativistic flows on curved stationary backgrounds.
发表机构
- University of Notre Dame（圣母大学）
- Duke University（杜克大学）
机构由 AI 辅助整理，请以论文原文为准。
