Saved in:
Bibliographic Details
Main Authors: Dong, Shanshan, Wang, Lu, Chen, Xiangxiang, Wang, Guanqing
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.00017
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917053201383424
author Dong, Shanshan
Wang, Lu
Chen, Xiangxiang
Wang, Guanqing
author_facet Dong, Shanshan
Wang, Lu
Chen, Xiangxiang
Wang, Guanqing
contents The discretization of velocity space plays a crucial role in the accuracy and efficiency of multiscale Boltzmann solvers. Conventional velocity space discretization methods suffer from uneven node distribution and mismatch issues, limiting the performance of numerical simulations. To address this, a Gaussian quadrature scheme with a parameterized weight function is proposed, combined with a polar coordinate transformation for flexible discretization of velocity space. This method effectively mitigates node mismatch problems encountered in traditional approaches. Numerical results demonstrate that the proposed scheme significantly improves accuracy while reducing computational cost. Under highly rarefied conditions, the proposed method achieves a speed-up of up to 50 times compared to the conventional Newton-Cotes quadrature, offering an efficient tool with broad applicability for numerical simulations of rarefied and multiscale gas flows.
format Preprint
id arxiv_https___arxiv_org_abs_2511_00017
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Two-dimensional Gauss--Jacobi Quadrature for Multiscale Boltzmann Solvers
Dong, Shanshan
Wang, Lu
Chen, Xiangxiang
Wang, Guanqing
Numerical Analysis
Fluid Dynamics
The discretization of velocity space plays a crucial role in the accuracy and efficiency of multiscale Boltzmann solvers. Conventional velocity space discretization methods suffer from uneven node distribution and mismatch issues, limiting the performance of numerical simulations. To address this, a Gaussian quadrature scheme with a parameterized weight function is proposed, combined with a polar coordinate transformation for flexible discretization of velocity space. This method effectively mitigates node mismatch problems encountered in traditional approaches. Numerical results demonstrate that the proposed scheme significantly improves accuracy while reducing computational cost. Under highly rarefied conditions, the proposed method achieves a speed-up of up to 50 times compared to the conventional Newton-Cotes quadrature, offering an efficient tool with broad applicability for numerical simulations of rarefied and multiscale gas flows.
title Two-dimensional Gauss--Jacobi Quadrature for Multiscale Boltzmann Solvers
topic Numerical Analysis
Fluid Dynamics
url https://arxiv.org/abs/2511.00017