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 chal...

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Bibliographic Details
Published in:	Journal of computational physics Vol. 522; p. 113619
Main Authors:	Li, Ruo, Lu, Yixiao, Wang, Yanli
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.02.2025
Subjects:	AP IMEX scheme Computation of polylogarithms Hermite spectral method Quantum BGK equation Computation of polylogarithms Hermite spectral method AP IMEX scheme Quantum BGK equation
ISSN:	0021-9991
Online Access:	Get full text
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Summary:	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. •Hermite spectral method for solving the quantum BGK equation.•Efficient algorithm to calculate the expansion coefficients of the quantum equilibrium.•Computation of the polylogarithm simplified to an one-dimensional numerical integration.•Asymptotic preserving property of the numerical scheme.•Lid-driven cavity flow to validate the high efficiency of this numerical method.
ISSN:	0021-9991
DOI:	10.1016/j.jcp.2024.113619