Scholarlink

<p>We present a comprehensive formulation of the general-relativistic Euler equations in Gullstrand-Painlevé coordinates, providing a description of fluid dynamics that remains regular across the Schwarzschild event horizon. After establishing the system and examining its mathematical properties including well-posedness behaviour, Riemann invariants, and characteristic wave speeds, we obtain its stationary solutions in implicit form and analyze them in detail for a representative equation of state. Building on these results, we design high-order exactly well-balanced numerical schemes capable of preserving all stationary states of the system. Both first- and second-order methods are constructed. Extensive numerical experiments confirm the accuracy, robustness, and well-balanced behavior of the proposed schemes. The study offers both theoretical insight into relativistic fluid flows near black holes and practical tools for reliable long-term simulations in curved spacetimes.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Fully Well-Balanced Methods for Schwarzschild–Euler Equation in Gullstrand–Painlevé Coordinates

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月21日

查看全文
  • Ernesto Pimentel-García,
  • Samuel Santos-Pérez,
  • Isabel Cordero-Carrión,
  • Carlos Parés

摘要

We present a comprehensive formulation of the general-relativistic Euler equations in Gullstrand-Painlevé coordinates, providing a description of fluid dynamics that remains regular across the Schwarzschild event horizon. After establishing the system and examining its mathematical properties including well-posedness behaviour, Riemann invariants, and characteristic wave speeds, we obtain its stationary solutions in implicit form and analyze them in detail for a representative equation of state. Building on these results, we design high-order exactly well-balanced numerical schemes capable of preserving all stationary states of the system. Both first- and second-order methods are constructed. Extensive numerical experiments confirm the accuracy, robustness, and well-balanced behavior of the proposed schemes. The study offers both theoretical insight into relativistic fluid flows near black holes and practical tools for reliable long-term simulations in curved spacetimes.