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粘性Burgers方程的高阶精度半隐式WCNS方法

陈勋1,2, 蒋艳群1,2, 陈琦2, 张旭1, 胡迎港1   

  1. 1. 西南科技大学理学院, 模型与算法研究所, 绵阳 621010;
    2. 中国空气动力研究与发展中心, 绵阳 621000
  • 收稿日期:2020-10-26 出版日期:2022-03-14 发布日期:2022-03-07
  • 通讯作者: 蒋艳群,Email:jyq2005@mail.ustc.edu.cn
  • 基金资助:
    通信作者蒋艳群由国家数值风洞工程项目(NNW2018-ZT4A08)和国家自然科学基金项目(11872323)资助.

陈勋, 蒋艳群, 陈琦, 张旭, 胡迎港. 粘性Burgers方程的高阶精度半隐式WCNS方法[J]. 数值计算与计算机应用, 2022, 43(1): 76-87.

Chen Xun, Jiang Yanqun, Chen Qi, Zhang Xu, Hu Yinggang. HIGH-ORDER SEMI-IMPLICIT WCNS METHOD FOR BURGERS' EQUATION[J]. Journal on Numerica Methods and Computer Applications, 2022, 43(1): 76-87.

HIGH-ORDER SEMI-IMPLICIT WCNS METHOD FOR BURGERS' EQUATION

Chen Xun1,2, Jiang Yanqun1,2, Chen Qi2, Zhang Xu1, Hu Yinggang1   

  1. 1. Model and Algorithm Research Institute, Department of Mathematics, Southwest University of Science and Technology, Mianyang 621000, China;
    2. China Aerodynamics Research and Development Center, Mianyang 621000, China
  • Received:2020-10-26 Online:2022-03-14 Published:2022-03-07
Burgers方程为Navier-Stokes方程组的简化形式,在计算数学和计算流体力学领域中有着广泛应用.本文设计了粘性Burgers方程的高阶精度半隐式加权紧致非线性格式(WCNS),并给出了稳定性分析.方程对流项和粘性项分别采用五阶精度WCNS格式和四阶中心差分格式计算.半离散系统采用三阶精度IMEX Runge-Kutta方法计算,对流项和粘性项分别进行显式和隐式处理.数值结果表明IMEX Runge-Kutta WCNS格式可达到三阶时间精度和五阶空间精度,比显式TVD Runge-Kutta WCNS格式计算效率高,且具有高分辨率的激波捕捉能力.
Burgers' equations are a simplified form of incompressible Navier-Stokes equations and have been widely used in computational mathematics and computational fluid dynamics. This paper designs a high-order semi-implicit weighted compact nonlinear scheme (WCNS) for viscous Burgers' equations and gives the stability analysis of the designed scheme. The fifth-order WCNS and the fourth-order central difference scheme are used for the spatial discretization of convective terms and viscous terms. The third-order IMEX Runge-Kutta scheme is used for the time discretization of the semi-discrete system and convective terms are treated explicitly, while viscosity terms are treated implicitly. Numerical results show that the IMEX Runge-Kutta WCNS can achieve third-order accuracy in time and fifth-order accuracy in space. This semi-implicit WCNS is better than the TVD Runge-Kutta WCNS in terms of computational efficiency and has high-resolution shock-capturing ability.

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[1] 张旭, 蒋艳群, 陈勋, 胡迎港. 粘性Burgers方程的高阶隐式WCNS格式[J]. 数值计算与计算机应用, 2022, 43(2): 188-201.
[2] 杨宇博, 马和平. 广义空间分数阶Burgers方程的Legendre Galerkin-Chebyshev配置方法逼近[J]. 数值计算与计算机应用, 2017, 38(3): 236-244.
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