稀薄气体流的二阶粒子福克-普朗克模型

IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computer Physics Communications Pub Date : 2024-07-25 DOI:10.1016/j.cpc.2024.109323
Sanghun Kim, Woonghwi Park, Eunji Jun
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引用次数: 0

摘要

直接模拟蒙特卡罗(DSMC)方法已成为研究稀薄气体流动的有力工具。然而,要使 DSMC 方法有效,单元大小必须小于平均自由路径,时间步长必须小于平均碰撞时间。这些限制使得 DSMC 方法难以用于多尺度稀薄气体流动。在过去的十年中,人们一直在研究粒子福克-普朗克(FP)方法,以解决近连续状态下的计算成本问题。为了捕捉波尔兹曼方程的主要特征,人们提出了各种 FP 模型,如二次熵 FP(Quad-EFP)和椭圆统计 FP(ESFP)。然而,很少有研究清楚地证明 FP 方法比 DSMC 方法在不牺牲精度的情况下具有计算优势。这是因为传统的粒子 FP 方法采用的是一阶精度方案。本研究提出了一种统一的随机粒子 ESFP(USP-ESFP)模型。该模型提高了剪应力和热通量预测的精度。此外,粒子 FP 方法还引入了空间插值方案。数值测试案例包括弛豫问题、Couette 流、Poiseuille 流、速度扰动和绕圆柱体的高超音速流。结果表明,USP-ESFP 模型与分析结果和 DSMC 结果非常吻合。此外,与 DSMC 方法相比,USP-ESFP 模型对单元大小和时间步长的敏感性较低,因此对于所考虑的绕圆柱体的高超音速流动,速度提高了四倍。
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A second-order particle Fokker-Planck model for rarefied gas flows

The direct simulation Monte Carlo (DSMC) method has become a powerful tool for studying rarefied gas flows. However, for the DSMC method to be effective, the cell size must be smaller than the mean free path, and the time step smaller than the mean collision time. These constraints make it difficult to use the DSMC method in multiscale rarefied gas flows. Over the past decade, the particle Fokker-Planck (FP) method has been studied to address computational cost issues in the near-continuum regime. To capture the main features of the Boltzmann equation, various FP models have been proposed, such as the quadratic entropic FP (Quad-EFP) and the ellipsoidal statistical FP (ESFP). Nevertheless, few studies have clearly demonstrated that the FP method offers a computational advantage over the DSMC method without sacrificing accuracy. This is because conventional particle FP methods have employed first-order accuracy schemes. The present study proposes a unified stochastic particle ESFP (USP-ESFP) model. This model improves the accuracy of shear stress and heat flux predictions. Additionally, a spatial interpolation scheme is introduced to the particle FP method. The numerical test cases include relaxation problem, Couette flows, Poiseuille flows, velocity perturbation, and hypersonic flows around a cylinder. The results show that the USP-ESFP model agrees well with both analytical and DSMC results. Furthermore, the USP-ESFP model is found to be less sensitive to cell size and time step than the DSMC method, resulting in a factor of four speed-up for the considered hypersonic flow around a cylinder.

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来源期刊
Computer Physics Communications
Computer Physics Communications 物理-计算机:跨学科应用
CiteScore
12.10
自引率
3.20%
发文量
287
审稿时长
5.3 months
期刊介绍: The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.
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