图形处理器上的相对论流体力学
Relativistic hydrodynamics on graphics processing units
摘要：
流体力学计算已成功地用于研究夸克-胶子等离子体的体性质，特别是椭圆流和剪切粘性。然而，也有一些领域（例如，逐事件模拟流动波动和高阶流动谐波研究），进一步的进步是由于缺乏有效和精确的3+1D~程序。这个问题可以通过使用图形处理单元（GPU）计算来解决，与标准CPU模拟相比，GPU计算提供了前所未有的计算能力。在这项工作中，我们提出了一个实现3+1D理想流体动力学模拟的图形处理单元使用Nvidia CUDA框架。模拟中采用了MUSTA-FORCE（Multi STAge，First ORder CENTRAL，with a~slope limiter and MUSCL reconstruction）和WENO（Weighted Essentially Non-Oscillating）格式，分别具有二阶（MUSTA-FORCE）、五阶和七阶（WENO）精度。时域积分采用三阶龙格-库塔格式。我们的实现提高了约2个数量级的性能相比，一个~单线程程序。给出了1+ 1维激波管和3+ 1维椭球展开和类哈勃展开的数值模拟的算法检验。
英文摘要：
Hydrodynamics calculations have been successfully used in studies of the bulk properties of the Quark-Gluon Plasma, particularly of elliptic flow and shear viscosity. However, there are areas (for instance event-by-event simulations for flow fluctuations and higher-order flow harmonics studies) where further advancement is hampered by lack of efficient and precise 3+1D~program. This problem can be solved by using Graphics Processing Unit (GPU) computing, which offers unprecedented increase of the computing power compared to standard CPU simulations. In this work, we present an implementation of 3+1D ideal hydrodynamics simulations on the Graphics Processing Unit using Nvidia CUDA framework. MUSTA-FORCE (MUlti STAge, First ORder CEntral, with a~slope limiter and MUSCL reconstruction) and WENO (Weighted Essentially Non-Oscillating) schemes are employed in the simulations, delivering second (MUSTA-FORCE), fifth and seventh (WENO) order of accuracy. Third order Runge-Kutta scheme was used for integration in the time domain. Our implementation improves the performance by about 2~orders of magnitude compared to a~single threaded program. The algorithm tests of 1+1D~shock tube and 3+1D~simulations with ellipsoidal and Hubble-like expansion are presented.
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