SRLW方程的多辛Fourier谱格式及其守恒律

计算物理 ›› 2006, Vol. 23 ›› Issue (1): 25-31.

SRLW方程的多辛Fourier谱格式及其守恒律

孔令华¹, 曾文平², 刘儒勋¹, 孔令健³

1. 中国科学技术大学数学系, 安徽合肥 230026;
2. 华侨大学数学系, 福建泉州 362021;
3. 博达公路有限公司, 江西赣州 341000

收稿日期:2004-09-28 修回日期:2005-04-04 出版日期:2006-01-25 发布日期:2006-01-25
作者简介:孔令华(1977),男,江西赣州,博士生,从事计算流体力学方面的研究,中国科大东区数学系科学计算与应用几何实验室.
基金资助:
国家自然科学基金(No.10371118,90411009);中国科学技术大学2005年研究生创新基金;北京应用物理与计算数学研究所计算物理实验室项目;国务院侨办科研基金(No.02QZR07);科学与工程计算国家重点实验室(LSEC)资助项目

A Muitisymplectic Fourier Pseudo-spectral Scheme for the SRLW Equation and Conservation Laws

KONG Ling-hua¹, ZENG Wen-ping², LIU Ru-xun¹, KONG Ling-jian³

1. Math. Dept., University of Science and Technology of China, Hefei 230026, China;
2. Math. Dept., Huaqiao Univ., Quanzhou 362021, China;
3. Boda Highway Ltd., Ganzhou 341000, China

Received:2004-09-28 Revised:2005-04-04 Online:2006-01-25 Published:2006-01-25

摘要/Abstract

摘要： 通过引进正则动量,将对称正则长波方程(简称SRLW方程)转化成多辛形式的方程组,它具有多辛守恒律;介绍了空间方向满足周期边界条件的函数的Fourier谱目的;对SRLW方程的多辛方程组在空间方向利用Fourer谱目的,时间方向上应用Euler中点格式离散,得到其多辛Fourier拟谱格式;证明此格式的一些离散守恒律.用此格式模拟了SRLW方程的单个孤立波,还模拟了多个孤立波的追赶、碰撞和分离过程.

关键词: 多辛格式, SRLW方程, Fourier拟谱格式

Abstract: A multisympletic system for the symmetric regularized long wave (SRLW) equation is obtained with canconical momentum. The system satisfies the multisymplectic conservation law. A Fourier pseudo-spectral method which adapts to periodic boundary conditions in space is introduced. An Euler mid-point scheme in time and a Fourier pseudo-spactral method in space are used to the muhisymplectic formulation of the SRLW equation. It makes a multisymplectic Fourier pseudo-spectral scheme. Several discrete conservation laws of this scheme are proved; Numerical experiments are performed to simulate the single soliton solution. The chase, collision and separation of multi-soliton solutions are simulated.

Key words: multisymplectic scheme, SRLW equation, Fourier pseudo-spectral scheme

中图分类号:

O241.82

孔令华, 曾文平, 刘儒勋, 孔令健. SRLW方程的多辛Fourier谱格式及其守恒律[J]. 计算物理, 2006, 23(1): 25-31.

KONG Ling-hua, ZENG Wen-ping, LIU Ru-xun, KONG Ling-jian. A Muitisymplectic Fourier Pseudo-spectral Scheme for the SRLW Equation and Conservation Laws[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 23(1): 25-31.

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