扩展型动网格的Chebyshev有限谱方法

詹杰民; 李毓湘; 董志

doi:10.3879/j.issn.1000-0887.2011.03.012

扩展型动网格的Chebyshev有限谱方法

doi: 10.3879/j.issn.1000-0887.2011.03.012

中山大学应用力学与工程系,广州 510275;2.香港理工大学土木及结构工程系,香港

基金项目: 香港研究资助局基金资助项目(522007);国家海洋公益性行业科研专项基金资助项目(201005002)

详细信息

作者简介:
詹杰民(1963- ),男,广东人,教授,博士,博士生导师(联系人.Tel/Fax:+86-20-84111130;E-mail:stszjm@mail.sysu.edu.cn).

中图分类号: O351.2;O24
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出版历程
- 收稿日期: 2010-01-25
- 修回日期: 1900-12-30
- 刊出日期: 2011-03-15

Chebyshev Finite Spectral Method With Extended Moving Grids

Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China;

摘要

摘要: 给出了基于非均匀网格的Chebyshev有限谱方法．提出了可生成两种类型扩展型动网格的均布格式．一种类型的网格被用来提高波面附近的分辨率，另一种类型则用在梯度较大的流动区域．由于采用Chebyshev多项式作为基函数，该方法具有高阶精度．从上个时间步到当前时间步，两套不均匀网格间的物理量采用Chebyshev多项式插值．为使方法在时间离散方面保持高精度，采用了Adams-Bashforth预报格式和Adams-Moulton校正格式．为了避免由Korteweg-deVries(KdV)方程的弥散项引起的数值振荡，给出了一种非均匀网格下的数值稳定器．给出的方法与具有分析解的Burgers方程的非线性对流扩散问题和KdV方程的单孤独波和双孤独波传播问题进行了比较，结果非常吻合．
- Chebyshev多项式 /
- 有限谱方法 /
- 非线性波 /
- 非均匀网格 /
- 移动网格
Abstract: A Chebyshev finite spectral method on non-uniform mesh was proposed.An equidistribution scheme for two types of extended moving grids was proposed for grid generation.One type of grid was designed to provide better resolution for wave surface.The other type was for highly variable gradients.The method was of high-order accuracy because of the use of Chebyshev polynomial as the basis function.The polynomial was used to interpolate values between the two non-uniform meshes from the previous time step to the current time step.To attain high accuracy in time discretization,the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme was used.To avoid numerical oscillations caused by the dispersion term in the KdV equation,a numerical technique on non-uniform mesh was introduced to improve the numerical stability.The proposed numerical scheme was validated by applications to the Burgers equation (nonlinear convection-diffusion problem) and KdV equation (single solitary and 2-solitary wave problems),where analytical solutions were available for comparison.Numerical results agree very well with the corresponding analytical solutions in all cases.
- Chebyshev polynomial /
- finite spectral method /
- nonlinear wave /
- non-uniform mesh /
- moving grids

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参考文献(34)

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