宏观有限差异方案和一般传播多重放松时间格子博尔兹曼模型的修改方程
Ying Chen1, Xi Liu1, Zhenhua Chai1
1School of Mathematics and Statistics, <a href="https://ror.org/00p991c53">Huazhong University of Science and Technology</a>, Wuhan 430074, China; Institute of Interdisciplinary Research for Mathematics and Applied Science, <a href="https://ror.org/00p991c53">Huazhong University of Science and Technology</a>, Wuhan 430074, China; and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, <a href="https://ror.org/00p991c53">Huazhong University of Science and Technology</a>, Wuhan 430074, China.
这项研究介绍了一种新的通用传播多重放松时间格子博尔兹曼 (GPMRT-LB) 模型及其有限差异方案. 数字模拟证实了对流动-扩散和纳维埃-斯托克斯方程的第二和第四阶准确性.
科学领域:
- 计算流体动力学的流体动力学.
- 数字分析 数字分析
- 应用数学 应用数学 应用数学
背景情况:
- 格子博尔茨曼方法被广泛用于流体动力学模拟.
- 现有模型的准确性和适用于复杂方程的适用性可能受到限制.
- 对于精确的模拟,需要更高阶的精确数值方案至关重要.
研究的目的:
- 开发和分析一个新的通用传播多重放松时间格子博尔兹曼 (GPMRT-LB) 模型.
- 导出相应的宏观有限差异 (GPMFD) 方案.
- 调查各种缩放制度和方程的截断错误和修改方程 (ME).
主要方法:
- 开发GPMRT-LB模型和GPMFD计划.
- 马克斯韦代方法用于错误分析的应用.
- 对于非线性异型对流-扩散和纳维埃-斯托克斯方程的第一级和第二级ME的导数.
- 为特定的对流-扩散方程开发第四阶GPMRT-LB (F-GPMRT-LB) 和GPMFD (F-GPMFD) 方案.
主要成果:
- 对于基准问题,GPMRT-LB模型和GPMFD方案证明了二级空间准确性.
- 数字结果与分析解决方案有很好的一致性.
- 通过F-GPMRT-LB模型和1D CDE的F-GPMFD方案,在空间上实现了第四级的精度.
结论:
- 拟议的GPMRT-LB模型和GPMFD方案为流体动力学问题提供准确可靠的数值解决方案.
- 开发的第四阶方案为特定的对流-扩散方程提供了更高的准确性.
- 该研究通过基准问题模拟来验证理论分析.
更多相关视频
08:04Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
07:31Author Spotlight: Advancing Cell Membrane Biophysics - Exploring Interactions and Challenges Through Experimental and Computational Approaches
Published on: September 1, 2023
相关概念视频
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
Atomic Nuclei: Types of Nuclear Relaxation
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
Maxwell-Boltzmann Distribution: Problem Solving
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Mean free path and Mean free time
The de Broglie Wavelength
Maxwell's Thermodynamic Relations
All thermodynamic potentials are exact differentials. Therefore, their second-order...
