特征化积分格式的设计及其在浅水波问题中的应用

刘儒勋

特征化积分格式的设计及其在浅水波问题中的应用

刘儒勋

中国科技大学数学系

计量
- 文章访问数: 2365
- HTML全文浏览量: 179
- PDF下载量: 531
- 被引次数: 0
出版历程
- 收稿日期: 1989-10-11
- 刊出日期: 1992-03-15

The Design of Characterizing-lntegral Schemes and the Application to the Shallow Water Wave Problems

Liu Ru-xun

Department of Mathematics, University of Sci. & Tech. of China, Hefei

摘要

摘要: 本文介绍一种简单而又行之有效的顺风型格式——特征化积分格式的设计方法及应用技术,用这种方法设计的顺风型格式不受方程有型性的限制,容易推广,又能比较灵活地调节数值耗散性,使之适用不同的间断解的要求.本文利用这种方法作了非线性水波在岸上的变形、破碎过程的数值模拟.结果表明方法稳定、有效;同时作了二维溃坝灾害的数值模拟,表明方法向多维推广的简单、可行性.
- 特征线 /
- 数值模拟 /
- 浅水波问题
Abstract: In this paper a new approach for designing upwind type schemes-the characterizing-integral method and its applied skills are introduced. The method is simple, convenient and eff ective. And the method isn't only limited to conservation laws unlike other methods and maybe easily extended to multi-dimension problems. Furthermore, the numerical dissipation of the method can be flexibly regulated, so that it is especially suitable for solving various discontinuity problems.The paper shows us now to use this approach to simulate deformation and breaking of a nonlinear shallow water wave on a gentle slope, and to compute two-dimensional dam failure problem.
- characteristics /
- numerical simulation /
- shallow water wave

HTML全文

参考文献(20)

[1]	Lax, P. D., Shock wave and entropy, Proc. Symposium at the University of Winsconsin (1971).
[2]	Harten, A., On a class of high resolution total variation stable finite difference schemes. SIAM J. Numer. Anal., 21, (1984) 1.
[3]	Osher, S., Convergence of generalized MUSCL Schemes, SIAM J. Numer. Anal., 22, (1985) 947.
[4]	Munz, C-D., On the numerical dissipation of high resolution schemes for hyperbolic conservation laws, J. Comp. Phys., 77, (1988) 18.
[5]	Engquist, B. B., S. Osher, One sided difference approximations for nonlinear conservation laws, Math. of Comp., 36, (1980) 154.
[6]	刘儒勋、李百浩,中国科技大学学报,16(2)(1986),
[7]	刘儒勋、魏勇,计算物理,3(2) (1986),
[8]	刘儒勋、李百浩,计算物理,4(2)(1987).
[9]	忻孝康、刘儒勋、蒋伯诚,《计算流体力学》,国防科技大学出版社(1989).
[10]	刘儒勋、李百浩,中国科技大学华报,10(1) (1989).
[11]	Liu Ru-gun, ACTA Mathematics Scieutia, 10(1) (1990).
[12]	Liu Ru-gun, Acta Mathematics Scientia,(待发表)
[13]	王如云、刘儒勋,中国科技大学学报,20(1) (1990),
[14]	Glimm, J.,Comm, Pure&Appl.Math, 18 (1965),697,
[15]	刘儒勋.力学与实践,6(4) (1984).
[16]	唐建华.海洋学报,(6) (1984), 692,
[17]	邹光远、陈跃松.力学学报,21(1)(1989).
[18]	吴坚,刘儒勋、李百浩,计算物理.(待发表)Dušan Mićević,and Rusov Lazar,Nove forme Jednačina analitičke mechanike,Зб.Раб.Mam.Ин-m,Београд,4(1984),139-148..
[19]	Kinnmark, I.,The shallow water wave eguations:formulation,analysis and application,Lecture Notes in Engsneering(13) (1985).
[20]	文圣常、余宙文,《海浪理论与计算原理》,科学出版社(1985).