• 论文 • 上一篇    

非线性消去算法在跨音速全速势方程计算中的应用

周佳敏1, 刘璐璐1, 余瀚2,3   

  1. 1. 南京理工大学, 数学与统计学院, 南京 210094;
    2. 南京邮电大学, 江苏省大数据安全与智能处理重点实验室, 南京 210023;
    3. 苏州科达科技股份有限公司, 苏州 215011
  • 收稿日期:2021-07-16 发布日期:2022-12-08
  • 基金资助:
    国家自然科学基金(11901296), 江苏省自然科学基金(BK20180450), 中国博士后科学基金项目(2021M692367)和江苏省博士后科研项目(2021K475C)资助.

周佳敏, 刘璐璐, 余瀚. 非线性消去算法在跨音速全速势方程计算中的应用[J]. 数值计算与计算机应用, 2022, 43(4): 425-446.

Zhou Jiamin, Liu Lulu, Yu Han. APPLICATION OF NONLINEAR ELIMINATION IN SOLVING THE TRANSONIC FULL POTENTIAL EQUATION[J]. Journal on Numerica Methods and Computer Applications, 2022, 43(4): 425-446.

APPLICATION OF NONLINEAR ELIMINATION IN SOLVING THE TRANSONIC FULL POTENTIAL EQUATION

Zhou Jiamin1, Liu Lulu1, Yu Han2,3   

  1. 1. School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China;
    2. Jiangsu Key Laboratory of Big Data Security & Intelligent Processing, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
    3. Suzhou Keda Technology Company Ltd., Suzhou 215011, China
  • Received:2021-07-16 Published:2022-12-08
基于非线性消去技术,构造了跨音速全速势方程的并行非线性求解器.首先详细阐述了跨音速全速势方程及其有限差分格式.其次,借助非线性消去技术,通过隐式消去局部强非线性的方式,改善牛顿迭代法的全局收敛性质,从而在激波存在的情况下达到加速收敛的目的.最后,研究了马赫数、网格大小、处理器个数以及局部子问题求解精度等参数对算法收敛情况和总计算时间的影响.数值结果表明,提出的右侧非线性预条件算法在求解全速势方程时具有很好的鲁棒性和可扩展性.
Based on nonlinear elimination, a parallel nonlinear solver is developed to simulate the flows for the transonic full potential equation. Firstly, we present the transonic full potential equation and its finite difference discretization in detail. Secondly, the local high nonlinearities are removed implicitly by nonlinear elimination in order to improve the global convergence performance of the Newton iterative method, so that fast convergence can be obtained even when the shock occurs. Finally, we study the effects of the Mach number, the mesh size, the number of processors, and the relative tolerance for the local subproblems on the convergence performance and the total execution time. Numerical results demonstrate that the right nonlinear preconditioned algorithm performs well to solve the full potential equation in terms of robustness and scaling.

MR(2010)主题分类: 

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