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Main Authors: Wang, Lu, Deng, Lingyun, Wang, Guanqing, Liang, Hong, Xu, Jiangrong
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2510.19624
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author Wang, Lu
Deng, Lingyun
Wang, Guanqing
Liang, Hong
Xu, Jiangrong
author_facet Wang, Lu
Deng, Lingyun
Wang, Guanqing
Liang, Hong
Xu, Jiangrong
contents The discrete velocity method (DVM) is a powerful framework for simulating gas flows across continuum to rarefied regimes, yet its efficiency remains limited by existing quadrature rules. Conventional infinite-domain quadratures, such as Gauss-Hermite, distribute velocity nodes globally and perform well near equilibrium but fail under strong nonequilibrium conditions. In contrast, finite-interval quadratures, such as Newton-Cotes, enable local refinement but lose efficiency near equilibrium. To overcome these limitations, we propose a generalized Gauss-Jacobi quadrature (GGJQ) for DVM, built upon a new class of adjustable weight functions. This framework systematically constructs one- to three-dimensional quadratures and maps the velocity space into polar or spherical coordinates, enabling flexible and adaptive discretization. The GGJQ accurately captures both near-equilibrium and highly rarefied regimes, as well as low- and high-Mach flows, achieving superior computational efficiency without compromising accuracy. Numerical experiments over a broad range of Knudsen numbers confirm that GGJQ consistently outperforms traditional Newton-Cotes and Gauss-Hermite schemes, offering a robust and efficient quadrature strategy for multiscale kinetic simulations.
format Preprint
id arxiv_https___arxiv_org_abs_2510_19624
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Generalized Gauss-Jacobi rules for discrete velocity method in Multiscale Flow Simulations
Wang, Lu
Deng, Lingyun
Wang, Guanqing
Liang, Hong
Xu, Jiangrong
Fluid Dynamics
The discrete velocity method (DVM) is a powerful framework for simulating gas flows across continuum to rarefied regimes, yet its efficiency remains limited by existing quadrature rules. Conventional infinite-domain quadratures, such as Gauss-Hermite, distribute velocity nodes globally and perform well near equilibrium but fail under strong nonequilibrium conditions. In contrast, finite-interval quadratures, such as Newton-Cotes, enable local refinement but lose efficiency near equilibrium. To overcome these limitations, we propose a generalized Gauss-Jacobi quadrature (GGJQ) for DVM, built upon a new class of adjustable weight functions. This framework systematically constructs one- to three-dimensional quadratures and maps the velocity space into polar or spherical coordinates, enabling flexible and adaptive discretization. The GGJQ accurately captures both near-equilibrium and highly rarefied regimes, as well as low- and high-Mach flows, achieving superior computational efficiency without compromising accuracy. Numerical experiments over a broad range of Knudsen numbers confirm that GGJQ consistently outperforms traditional Newton-Cotes and Gauss-Hermite schemes, offering a robust and efficient quadrature strategy for multiscale kinetic simulations.
title Generalized Gauss-Jacobi rules for discrete velocity method in Multiscale Flow Simulations
topic Fluid Dynamics
url https://arxiv.org/abs/2510.19624