计算机应用 ›› 2012, Vol. 32 ›› Issue (10): 2745-2747.DOI: 10.3724/SP.J.1087.2012.02745

• 先进计算 • 上一篇    下一篇

二维双曲守恒律标量方程的三阶CWENO-型熵相容算法

郑素佩1,封建湖1,刘彩侠2   

  1. 1. 长安大学 理学院,西安 710064
    2. 河南工业大学 理学院,郑州 450001
  • 收稿日期:2012-04-05 修回日期:2012-05-21 发布日期:2012-10-23 出版日期:2012-10-01
  • 通讯作者: 郑素佩
  • 作者简介:郑素佩(1978-),女,河南许昌人,讲师,博士,主要研究方向:偏微分方程数值解法、计算流体力学;封建湖(1960-),男,陕西子洲人,教授,博士,主要研究方向:偏微分方程数值解法、计算流体力学、图像处理;刘彩侠(1978-),女,河南夏邑人,讲师,硕士,主要研究方向:偏微分方程数值解法、空气动力学。
  • 基金资助:
    国家自然科学基金资助项目;中央高校基本科研业务费资助项目

CWENO-type entropy consistent scheme for two dimensional scalar hyperbolic conservation laws

ZHENG Su-pei1,FENG Jian-hu1,LIU Cai-xia2   

  1. 1. School of Science, Chang’an University, Xi’an Shaanxi 710064, China
    2. School of Science, Henan University of Technology, Zhengzhou Henan 450001, China
  • Received:2012-04-05 Revised:2012-05-21 Online:2012-10-23 Published:2012-10-01
  • Contact: ZHENG Su-pei

摘要: 应用提出的中心加权基本无振荡(CWENO)-型熵相容格式求解了二维双曲守恒律方程初边值问题,对所得数值结果进行了分析与讨论,并通过与准确解的比较发现该数值求解格式稳定性条件可以取到0.6,而激波过渡带只有1~2个网格单元。实验结果表明该数值求解格式分辨率高且数值稳定性好。

关键词: 熵守恒格式, 熵相容格式, 三阶优化龙格库塔方法, 半离散, 双曲守恒律

Abstract: This paper advanced the Central Weighted Essentially Nonoscillatory (CWENO)-type entropy consistent schemes to simulate the two-dimensional conservation laws of the initial boundary value problem. The numerical results were analyzed and compared with the exact solutions. It is pointed out that the courant-friedrich-lewy can attain 0.6 and shock transition zone is one or two cells. The results indicate that the new numerical method in this paper has high-resolution and strong stability.

Key words: entropy conservative schemes, entropy consistent schemes, third order optimal Runge-Kutta method, semi-discrete, hyperbolic conservation laws

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