摘要
该文基于一致高精度紧致格式概念,针对对流扩散方程提出了一种改进的一致四阶紧致格式,该格式在时间方向上采用TVD型的三阶Runge-Kutta方法,在空间方向上采用改进的一致四阶紧致格式,并对此半离散格式进行了渐近稳定性分析.在求解对流占优问题时,该文提出的边界格式相较于一致四阶紧致格式,在减少数值振荡方面取得了不错的效果.此外,通过驱动方腔的数值模拟结果表明:该格式在求解不可压N-S方程组方面展现了较高的精确性和有效性.这些结果进一步证实了该格式在模拟和研究复杂流体流动方面的适用性和可靠性.
Based on the concept of high-order and consistent compact scheme,the improved consistent fourth-order compact scheme for the convective diffusion equation is presented.It employs a TVD-type third-order Runge-Kutta method for the time direction and an enhanced consistent fourth-order compact scheme for the spatial direction.The stability of this semi-discrete scheme is analyzed asymptotically.Compared to the traditional consistent fourth-order compact scheme,the boundary scheme proposed in this paper effectively reduces numerical oscillations when addressing convection-dominated problems.Additionally,numerical simulation results for the driven cavity show that this scheme demonstrates high accuracy and effectiveness in solving the incompressible Navier-Stokes equations.These findings further affirm the applicability and reliability of this scheme in simulating and studying complex fluid flows.
作者
刘俊
王涛
LIU Jun;WANG Tao(School of Mathematics and Information Science,North Minzu University,Ningxia Yinchuan 750021,China)
出处
《江西师范大学学报(自然科学版)》
北大核心
2025年第2期213-220,F0003,共9页
Journal of Jiangxi Normal University(Natural Science Edition)
基金
国家自然科学基金(12162001)
宁夏自然科学基金(2023AAC03286)资助项目
关键词
改进的一致四阶格式
渐近稳定性
对流占优
驱动方腔
improved consistent fourth-order scheme
the asymptotic stability
convection-dominated
driven square cavity
