Free Boundary Problem of Non-Steady State Seepage Flow

Sun Ying; Guo Xiaoming; She Yinghe

Volume 20 Issue 7

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(7): 756-760

Sun Ying, Guo Xiaoming, She Yinghe. Free Boundary Problem of Non-Steady State Seepage Flow[J]. Applied Mathematics and Mechanics, 1999, 20(7): 756-760.

Citation:

Sun Ying, Guo Xiaoming, She Yinghe. Free Boundary Problem of Non-Steady State Seepage Flow[J]. Applied Mathematics and Mechanics, 1999, 20(7): 756-760.

Citation:

Sun Ying, Guo Xiaoming, She Yinghe. Free Boundary Problem of Non-Steady State Seepage Flow[J]. Applied Mathematics and Mechanics, 1999, 20(7): 756-760.

PDF( 1720 KB)

Free Boundary Problem of Non-Steady State Seepage Flow

1.
Nanjing Engineering Institute, Nanjing 210007, P R China;
2.
Southeast University, Nanjing 210096, P R China

Received Date: 1997-10-21
Rev Recd Date: 1999-04-07
Publish Date: 1999-07-15

Abstract

Abstract

Along with the vigorous developing construction,the number of various underground engineerings is greatly increasing,such as the foundations of dams and high-rise dmultistored hauses,the subways and the tunnels,the water and oil wells etc.,where the close attention is always paid to the seepage behaviour in the media around the structures.In Appl.Math Mech.1996,17(6),the variational inequality formulation and its FEM solution for the free boundary problem of 2D steady state seepage flow was given by She Yinghe et al.In this paper a further investigation is made on the non-steady state seepage problem,by taking the seepage flow of wells as an example.The presented approach——variational inequality and its FEM solution——is also very beneficial to the non-steady state problems,where the transient free boundary can also be defined directly without conventional iterations.
- seepage,
- non-steady state,
- variational inequality

FullText(HTML)

References(4)

References

[1]	Huang S, Zhou C. Numerical solution of non-steady state porous flow free boundary problems[J]．Journal of Computational Mathematics,1985,3(1):72～89.
[2]	Torelli A. On a free boundary value problem connected with a non-steady filtration phenomenon[J].Ann Scu Norm Sup Prsa,1977,4(1):33～59.
[3]	张柔雷,佘颍禾.用变步长有限元法求解暂态温度场[J].南京工学院学报,1984,14(2):1～10．
[4]	佘颍禾,孙鹰,郭小明.具有自由边界的二维渗流问题[J].应用数学和力学,1996,17(6):523～527.

Relative Articles

[1]	WANG Xiaoting, LONG Xianjun, PENG Zaiyun. A Double Projection Algorithm for Solving Non-Monotone Variational Inequalities[J]. Applied Mathematics and Mechanics, 2022, 43(8): 927-934. doi: 10.21656/1000-0887.420414
[2]	YANG Jun. A Golden Ratio Algorithm for Solving Nonmonotone Variational Inequalities[J]. Applied Mathematics and Mechanics, 2021, 42(7): 764-770. doi: 10.21656/1000-0887.410359
[3]	LIU Ying. Strong Convergence Theorems for Relatively Nonexpansive Mappings and Inverse-Strongly-Monotone Mappings in a Banach Space[J]. Applied Mathematics and Mechanics, 2009, 30(7): 865-872. doi: 10.3879/j.issn.1000-0887.2009.07.011
[4]	HU Yan-hong, SONG Wen. Generalized Gap Functions and Error Bounds for Generalized Variational Inequalities[J]. Applied Mathematics and Mechanics, 2009, 30(3): 301-308.
[5]	DING Xie-ping, LIN Yen-cherng, YAO Jen-chih. Three-Step Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities[J]. Applied Mathematics and Mechanics, 2007, 28(8): 921-928.
[6]	GUO Da-li, ZENG Xiao-hui, ZHAO Jin-zhou, LIU Ci-qun4. Model and Method of Well Test Analysis for Wells With Vertical Fracture[J]. Applied Mathematics and Mechanics, 2005, 26(5): 527-533.
[7]	ZHENG Hong, LIU De-fu, LEE C. F., THAM L. G.. New Variational Inequality Formulation for Seepage Problems With Free Surfaces[J]. Applied Mathematics and Mechanics, 2005, 26(3): 363-371.
[8]	ZHANG Shi-sheng. Multi-Valued Quasi Variational Inclusions in Banach Spaces[J]. Applied Mathematics and Mechanics, 2004, 25(6): 572-580.
[9]	WANG Zheng-yu, SHEN Zu-he. Kantorovich Theorem for Variational Inequalities[J]. Applied Mathematics and Mechanics, 2004, 25(11): 1182-1188.
[10]	GUO Xing-ming, ZHOU Shi-xing. Optimal Control of Parabolic Variational Inequalities With Stat Constraint[J]. Applied Mathematics and Mechanics, 2003, 24(7): 669-674.
[11]	TONG Deng-ke, Zhang Hong-qing. The Flow Problem of Fluids Flow in a Fractal Reservoir With Double Porosity[J]. Applied Mathematics and Mechanics, 2001, (10): 1009-1016.
[12]	Xi Zhizhong. Mechanism in Pneumotransport of the Fibroid Substance[J]. Applied Mathematics and Mechanics, 1999, 20(4): 381-385.
[13]	Gao Yang. Contact Problems and Dual Variational Inequality of 2-D Elastoplastic Beam Theory[J]. Applied Mathematics and Mechanics, 1996, 17(10): 895-908.
[14]	She Yinghe, Sun Ying, Guo Xiaoming. Free Boundary Problem of the 2D Seepage Flow[J]. Applied Mathematics and Mechanics, 1996, 17(6): 523-527.
[15]	Zheng Tie-sheng, Li Li, Xu Qing-yu. An Iterative Method for the Discrete Problems of a Class of Elliptical Variational Inequalities[J]. Applied Mathematics and Mechanics, 1995, 16(4): 329-335.
[16]	Zhang Shi-sheng, Zhang Yin. Section Theorems, Coincidence Theorems and Intersection Theorems on H-Spaces with Applications[J]. Applied Mathematics and Mechanics, 1993, 14(9): 763-774.
[17]	Guo Xiao-ming, She Ying-he. The Variational Inequality Formulation for the Deformation Theory in Plasticity and Its Non-Iterative Solution[J]. Applied Mathematics and Mechanics, 1993, 14(12): 1105-1113.
[18]	Wang Xiang-dong, Liang Xi-ting. The Holder Continuity for the Gradient of Solutions to One-Sided Obstacle Problems[J]. Applied Mathematics and Mechanics, 1992, 13(9): 811-820.
[19]	Zhang Shi-sheng, Xiang Shu-wen. On the Existence and Uniqueness of Solutions for a Class of Variational Inequalities with Applications to the Signorini Problem in Mechanics[J]. Applied Mathematics and Mechanics, 1991, 12(5): 401-407.
[20]	Sha De-song, Sun Huan-chun, Xu Shou-ze. Formulation of Boundary Element-Linear Complementary Equation for the Ffictional Elastic Contact Problems[J]. Applied Mathematics and Mechanics, 1990, 11(12): 1035-1041.