采用隐式 Runge-Kutta 方法的相对论流体力学高效求解器

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
Nathan Touroux, Masakiyo Kitazawa, Koichi Murase, Marlene Nahrgang
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引用次数: 0

摘要

我们提出了一种基于隐式 Runge-Kutta 方法和局部优化定点迭代求解器求解相对论流体力学方程的新方法。为了进行数值演示,我们使用单级高斯-列根德雷法作为隐式方法,在理想流体力学中实现了我们的想法。我们将新方法的精度和计算成本与显式方法进行了比较,前者适用于 (1+1)-dimensional 黎曼问题,后者适用于 (2+1)-dimensional Gubser 流和 TRENTo 生成的重离子碰撞的逐事件初始条件。我们证明,在大多数情况下,求解器只需一次迭代就能收敛,因此,在这些情况下,在相同精度下,隐式方法比显式方法所需的计算成本更低,同时,隐式方法可能不会在Δt过大的情况下收敛。通过展示带有迭代求解器的单步高斯-列根德雷法与两步亚当斯-巴什福斯法之间的关系,我们认为我们的方法同时受益于前者的稳定性和后者的高效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Efficient solver of relativistic hydrodynamics with implicit Runge-Kutta method
We propose a new method to solve the relativistic hydrodynamic equations based on implicit Runge-Kutta methods with a locally optimized fixed-point iterative solver. For numerical demonstration, we implement our idea for ideal hydrodynamics using the one-stage Gauss-Legendre method as an implicit method. The accuracy and computational cost of our new method are compared with those of explicit ones for the (1+1)-dimensional Riemann problem, as well as the (2+1)-dimensional Gubser flow and event-by-event initial conditions for heavy-ion collisions generated by TRENTo. We demonstrate that the solver converges with only one iteration in most cases, and as a result, the implicit method requires a smaller computational cost than the explicit one at the same accuracy in these cases, while it may not converge with an unrealistically large Δt. By showing a relationship between the one-stage Gauss-Legendre method with the iterative solver and the two-step Adams-Bashforth method, we argue that our method benefits from both the stability of the former and the efficiency of the latter.
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CiteScore
7.20
自引率
4.30%
发文量
567
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