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Updated: Jul 26, 2025

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第四次多重放松时间格子博尔茨曼模型和等效的有限差异方案为一维的对流-扩散方程
Ying Chen1, Zhenhua Chai1,2,3, Baochang Shi1,3
1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
Physical review. E
|June 17, 2023
概括
为对流-扩散方程 (CDE) 开发了一种新的第四次多重放松时间格子博尔茨曼模型 (MRT-LB) 和一个四级有限差异 (FLFD) 方案. 数字结果证实了他们的第四阶空间精度.
科学领域:
- 计算物理学的计算物理.
- 数字分析 数字分析
背景情况:
- 对流-扩散方程 (CDE) 在模拟运输现象方面是至关重要的.
- 准确和高效的数值方法对于解决CDE至关重要.
研究的目的:
- 为一维CDE开发一个第四阶准确的多重放松时间格子博尔兹曼 (MRT-LB) 模型.
- 从MRT-LB模型中推导出一个明确的四级有限差异 (FLFD) 方案.
- 分析开发方法的稳定性和准确性.
主要方法:
- 基于D1Q3格子的MRT-LB模型的开发.
- 查普曼-恩斯科格分析以收回CDE.
- 一个明确的FLFD计划的衍生.
- 泰勒扩展用于截断错误分析.
- 稳定性分析. 稳定性分析.
主要成果:
- 为1D CDE成功开发了MRT-LB模型和FLFD方案.
- 在扩散缩放下,FLFD方案在空间中实现了四级精度.
- 稳定性分析证实,这两种方法的稳定性条件相同.
- 数字实验证明了空间中的第四阶融合率.
结论:
- 开发的MRT-LB模型和FLFD方案为1D CDE提供了准确和稳定的数值解决方案.
- 这些发现与理论分析一致,验证了方法的有效性.
- 这项工作为对流-扩散问题提供了高效的计算工具.
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