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

Liu Ru-xun

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(3): 215-222

Liu Ru-xun. The Design of Characterizing-lntegral Schemes and the Application to the Shallow Water Wave Problems[J]. Applied Mathematics and Mechanics, 1992, 13(3): 215-222.

Citation:

Liu Ru-xun. The Design of Characterizing-lntegral Schemes and the Application to the Shallow Water Wave Problems[J]. Applied Mathematics and Mechanics, 1992, 13(3): 215-222.

Citation:

Liu Ru-xun. The Design of Characterizing-lntegral Schemes and the Application to the Shallow Water Wave Problems[J]. Applied Mathematics and Mechanics, 1992, 13(3): 215-222.

PDF( 488 KB)

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

Received Date: 1989-10-11
Publish Date: 1992-03-15

Abstract

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

FullText(HTML)

References(20)

References

[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).