Regularized lattice Boltzmann model for one-dimensional nonlinear scalar hyperbolic conservation laws

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-09-19 DOI:10.1016/j.aml.2025.109764

Yixuan Ge , Zhenyu Chen , Baochang Shi , Yong Zhao

引用次数: 0

Abstract

In this paper, we propose a regularized lattice Boltzmann model for one-dimensional nonlinear scalar hyperbolic conservation laws which can convert to convection–diffusion equation through introducing a dissipation term. Then, a rigorous Chapman–Enskog analysis is conducted to show that this models can recover the correct governing equation. Finally, we also conduct some simulations to test the model and find that the numerical results not only agree with the exact solutions but also exhibits superior performance in solving hyperbolic conservation laws with discontinuous initial conditions.

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一维非线性标量双曲守恒律的正则晶格玻尔兹曼模型

本文提出了一维非线性标量双曲守恒律的正则晶格玻尔兹曼模型，该模型通过引入耗散项可转化为对流扩散方程。然后，进行了严格的Chapman-Enskog分析，表明该模型可以恢复正确的控制方程。最后，通过仿真对模型进行了验证，结果表明，数值结果不仅与精确解相符，而且在求解初值不连续的双曲型守恒律时也表现出较好的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.