量子BGK方程的一种高效渐近保持IMEX方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics Pub Date : 2024-11-26 DOI:10.1016/j.jcp.2024.113619

Ruo Li , Yixiao Lu , Yanli Wang

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引用次数: 0

摘要

本文提出了一种用Hermite谱法求解量子BGK方程的渐近保持（AP）隐显（IMEX）格式。将分布函数展开为一系列厄米特多项式，高斯函数作为权函数。该数值格式的主要挑战在于用厄米特基函数有效地展开量子麦克斯韦方程组。为了克服这个问题，我们将问题简化为多对数的计算，并提出了一种有效的算法来处理它，利用高斯-埃尔米特正交。若干数值模拟，包括空间二维盖子驱动的空腔流动，证明了该方法的AP特性和显著的效率。

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A highly efficient asymptotic preserving IMEX method for the quantum BGK equation

This paper presents an asymptotic preserving (AP) implicit-explicit (IMEX) scheme for solving the quantum BGK equation using the Hermite spectral method. The distribution function is expanded in a series of Hermite polynomials, with the Gaussian function serving as the weight function. The main challenge in this numerical scheme lies in efficiently expanding the quantum Maxwellian with the Hermite basis functions. To overcome this, we simplify the problem to the calculation of polylogarithms and propose an efficient algorithm to handle it, utilizing the Gauss-Hermite quadrature. Several numerical simulations, including a spatially 2D lid-driven cavity flow, demonstrate the AP property and remarkable efficiency of this method.

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来源期刊

Journal of Computational Physics 物理-计算机：跨学科应用

CiteScore

7.60

自引率

14.60%

发文量

763

审稿时长

5.8 months

期刊介绍： Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.