The Mathematical Modelling of Near Coast Shallow Water Circulation

Lü Yu-lin; Lai Guo-zhang

Volume 5 Issue 5

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1984 > 5(5): 731-742

Lü Yu-lin, Lai Guo-zhang. The Mathematical Modelling of Near Coast Shallow Water Circulation[J]. Applied Mathematics and Mechanics, 1984, 5(5): 731-742.

Citation:

Lü Yu-lin, Lai Guo-zhang. The Mathematical Modelling of Near Coast Shallow Water Circulation[J]. Applied Mathematics and Mechanics, 1984, 5(5): 731-742.

Citation:

Lü Yu-lin, Lai Guo-zhang. The Mathematical Modelling of Near Coast Shallow Water Circulation[J]. Applied Mathematics and Mechanics, 1984, 5(5): 731-742.

PDF( 668 KB)

The Mathematical Modelling of Near Coast Shallow Water Circulation

Dalian Institute of Technology, Dalian

Received Date: 1982-12-27
Publish Date: 1984-10-15

Abstract

Abstract

This paper presents a finite element method to solve the shallow water circulation problem numerically.Considering the Coriolis effect,bottom friction and eddy viscosity,the continuity equation and momentum equation are integrated vertically. Using Galerkin weighted residual method,the weak variational formulation is derived for the finite element analysis. The split-time method is applied for the numerical integration instead of iteration for nonlinear terms. Moreover,an artificial smooth approach is proposed to suppress the short wavelength noise.In order to save computer storage units,a densed storage scheme is set up,where all the zero elements in large scaled and sparse matrices are excluded.

FullText(HTML)

References(11)

References

[1]	Leendertse,J.J.,Aspects of a Computational model for long period water wave propagation,Rand Corp.RM-5294-PR,(1967).
[2]	金子史雄、崛江毅、村上和男.ADI法による潮流污染掂散の数值酬算—大阪湾に遭用した场合につひこ.港湾技衔研究所银告,14,1(1975).
[3]	Liggett,J.A.and D.A.Woolhiser,DifFerence solutions of the shallow water equation,Jour.Engng.Mech.Division,ASME,EM2,April,(1967).
[4]	Taylor,C.and J.Davis,Tidal and long water propagation-A finite element approach,Computers and Fluids,Vol.3,(1975).
[5]	Connor,J.J.and J.D.Wang,Mathematical models of the Massachusetts Bay,Part I,MIT Sea Grant Technical Report,MITSG 74-4,(1973).
[6]	Easton,A.K.and H.R.Milner,Comparison of two tidal model for Cario Bay,Victoria Finite Element Methods is Engineering,Dec.(1976).
[7]	Kawahare,M.,A.Takeuchi and T.Yoshida,Two step explicit finite element method for Tsunami wave propagation analysis,Int.J.Num.Meth.Engng.Vol.12,No.2,(1978).
[8]	Gray,W.G.and D.R.Lynch,On the control of noise in finite element tidal computations,Computers and Fluids,Vol.7,No.3.March,(1979).
[9]	Grotkop,G.,Finite element analysis of long-period water waves,Comp.Math.in Appl.Mech.and Engng.,Vol 2,(1973).
[10]	Norton,W.R.,I.P.King and G.T.Orlob,A finite element model for lower granite reservoir,Water Resources,Engineers Inc.,Walnut Creek,(1973).
[11]	Withum,D.,K.P.Holz and U.Meissner,Finite element formulations for tidal wave analysis,Computer Methods in Applied Mechanics and Engineering,17/18(1979).

Relative Articles

[1]	FAN Yajie, LI Yan, LI Zhongpan, CHEN Huijian, FENG Zhiqiang. Smoothed Finite Element Analysis of Contact and Large Deformation Problems[J]. Applied Mathematics and Mechanics, 2024, 45(2): 127-143. doi: 10.21656/1000-0887.440251
[2]	WANG Ke-yong, HUANG Zheng-ming, LI Pei-chao, LIU Bo. Trefftz Finite Element Analysis of Axisymmetric Potential Problems in Orthotropic Media[J]. Applied Mathematics and Mechanics, 2013, 34(5): 462-469. doi: 10.3879/j.issn.1000-0887.2013.05.004
[3]	YANG Yong-qin, XIAO Liu-chao, CHEN Shao-chun. Nonconforming Finite Elements for the Equation of Planar Elasticity[J]. Applied Mathematics and Mechanics, 2010, 31(12): 1454-1464. doi: 10.3879/j.issn.1000-0887.2010.12.006
[4]	LIU You-wen, FANG Qi-hong. Adaptive Finite Element Method for Analysis of Pollutant Dispersion in Shallow WaterSomboon Otarawanna,Pramote Dechaumphai[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1425-1435.
[5]	Zhu Jufen, Zheng Gang, Wu Jinying. F.E.M. Analysis of Delamination Buckling in Composite Plates & Shells[J]. Applied Mathematics and Mechanics, 2000, 21(3): 301-306.
[6]	Yan Bo, Liu Zhanfang, Zhang Xiangwei. Finite Element Analysis of Wave Propagation in Fluid-Saturated Porous Media[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1235-1244.
[7]	Ma Jinghuai. The Optimal Control Variational Principle and Finite Elements Analysis for Viscoplastic Dynamics[J]. Applied Mathematics and Mechanics, 1997, 18(1): 61-66.
[8]	Chen Dapeng, Zhang Jianhai. A Comparative Study of the Opening and Closing Process of Two Types of Mechanical Heart Valves Using ALE Finite Element Method[J]. Applied Mathematics and Mechanics, 1996, 17(4): 287-296.
[9]	Zhang Jianhai, Chen Dapeng, Zou Shengquan. ALE Finite Element Analysis of the Opening and Closing Process of the Artificial Mechanical Valve[J]. Applied Mathematics and Mechanics, 1996, 17(5): 387-396.
[10]	Zhang Hong-wu, Zhong Wan-xie, Qian Ling-xi. Finite Element Analysis for Consolidation in Interaction between Structure and Saturated Soil Foundation[J]. Applied Mathematics and Mechanics, 1992, 13(10): 891-899.
[11]	Chen Da-peng, Zhao Zhong. A Penalty-Hybrid Finite Element Analysis of Stokes Flow[J]. Applied Mathematics and Mechanics, 1990, 11(6): 467-476.
[12]	Li Long-yuan. The Rationalism Theory and Its Finite Element Analysis Method of Shell Structures[J]. Applied Mathematics and Mechanics, 1990, 11(4): 365-372.
[13]	Qian Yuan-yao. A Hybrid/Mixed Model Finite Element Analysis for Eigenvalue Problem of Moderately Thick Plates[J]. Applied Mathematics and Mechanics, 1987, 8(8): 733-742.
[14]	Zhang Shuang-yin, C. M. Leech. FEM Analysis on Mixed-Mode Fracture of CSM-GRP[J]. Applied Mathematics and Mechanics, 1986, 7(8): 689-702.
[15]	S. N. Atluri, Kuang Zhen-bang. A Finite Element Analysis for the Temperature Field Produced by a Moving Heat Source[J]. Applied Mathematics and Mechanics, 1986, 7(5): 383-400.
[16]	Liu Zheng-xing, Wu Lian-yuan, Feng Tai-hua. The Finite Element Analysis of the Flexible Beams and Plates[J]. Applied Mathematics and Mechanics, 1985, 6(9): 833-844.
[17]	Chien Wei-zhang. Diagonalized Consistant Mass Matrix and the Dynamical Finite Element Analysis of Elastic-Plastic Impact in Axisymmetrical Problems[J]. Applied Mathematics and Mechanics, 1982, 3(4): 429-448.
[18]	He Qiong, Cheng Zheng-ding, Xiong Huan-guo. Finite Element Study of Dynamic Characteristics of Main Components of Machine Tools[J]. Applied Mathematics and Mechanics, 1981, 2(6): 679-688.
[19]	On “Finite Element Analysis of Axisymmetric Elastic Body Problems”[J]. Applied Mathematics and Mechanics, 1980, 1(3): 417-417.
[20]	Chien Wei-zang. Finite Element Analysis of Axisymmetric Elastic Body Problems[J]. Applied Mathematics and Mechanics, 1980, 1(1): 25-35.