粘性Burgers方程的高阶精度半隐式WCNS方法

doi:10.12288/szjs.s2020-0710

数值计算与计算机应用 ›› 2022, Vol. 43 ›› Issue (1): 76-87.DOI: 10.12288/szjs.s2020-0710

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. 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.

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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 Xun^1,2, Jiang Yanqun^1,2, Chen Qi², Zhang Xu¹, Hu Yinggang¹

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.

关键词： Burgers方程, WCNS格式, IMEX Runge-Kutta方法, 计算效率, 激波捕捉

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.

Key words: Burgers' equations, WCNS, IMEX Runge-Kutta method, computational efficiency, shock-capturing

MR(2010)主题分类:

65M06
65N06

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[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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粘性Burgers方程的高阶精度半隐式WCNS方法

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

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