Viscous Flow With Free Surface Motion by Least Square Finite Element Method

TANG Bo; LI Jun-feng; WANG Tian-shu

Volume 29 Issue 7

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(7): 855-863

TANG Bo, LI Jun-feng, WANG Tian-shu. Viscous Flow With Free Surface Motion by Least Square Finite Element Method[J]. Applied Mathematics and Mechanics, 2008, 29(7): 855-863.

Citation:

TANG Bo, LI Jun-feng, WANG Tian-shu. Viscous Flow With Free Surface Motion by Least Square Finite Element Method[J]. Applied Mathematics and Mechanics, 2008, 29(7): 855-863.

Citation:

TANG Bo, LI Jun-feng, WANG Tian-shu. Viscous Flow With Free Surface Motion by Least Square Finite Element Method[J]. Applied Mathematics and Mechanics, 2008, 29(7): 855-863.

PDF( 401 KB)

Viscous Flow With Free Surface Motion by Least Square Finite Element Method

School of Aerospace, Tsinghua University, Beijing 100084, P. R. China

Received Date: 2007-11-08
Rev Recd Date: 2008-06-13
Publish Date: 2008-07-15

Abstract

Abstract

A method for simulation of free surface problems is presented.Based on the viscous incompressible Navier-Stokes equations,the space discretization of the flow was obtained by least square finite element method and the time evolution was obtained by finite difference method.Lagrangian description was used to track the free surface.The results here were compared with experimental dam break results,including water collapse in 2D rectangular section and in 3D cylinder section.Good agreement was achieved for the distance of surge front as well as the height of residual column.
- incompressible viscous fluid,
- Lagrangian description,
- least square finite element method,
- dam break experiment

FullText(HTML)

References(10)

References

[1]	吕敬,李俊峰,王天舒.带弹性附件充液矩形贮箱俯仰运动动态响应[J].应用数学和力学,2007,28(3):317-327.
[2]	Codina R. Pressure stability in fractional step finite element methods for incompressible flows[J].Journal of Computational Physics,2001,170(1):112-140. doi: 10.1006/jcph.2001.6725
[3]	Jiang B N.The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics[M].Berlin: Springer, 1998.
[4]	Brezzi F. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian mulipliears[J].Mathematical Modeling and Numerical Analysis,1974,8(2):129-151.
[5]	Guermond J L, Quartapelle L.On stability and convergence of projection methods based on pressure Poisson equation[J].International Journal for Numerical Methods in Fluids,1998,26(3):1039-1053. doi: 10.1002/(SICI)1097-0363(19980515)26:9<1039::AID-FLD675>3.0.CO;2-U
[6]	Hauashi M, Hatanaka K,Kawahara M.Lagrangian finite element method for free surface Navier-Stokes flow using fractional step methods[J].International Journal for Numerical Methods in Fluids,1991,13(7):805-840. doi: 10.1002/fld.1650130702
[7]	Oliver K H. Least-squares methods for the solution of fluid-structure interaction problems[D].Germany: TU Braunschweig, 2006.
[8]	Chang C L, Nelson J J.Least-squares finite element method for the stokes problem with zero residual of mass conservation[J].SIAM Journal on Numerical Analysis,1997,34(2):480-489. doi: 10.1137/S0097539794273368
[9]	Deang J M, Gunzburger M D.Issues related to least-squares finite element methods for the Stokes equations[J].SIAM Journal on Scientific Computing,1998,20(3):878-906. doi: 10.1137/S1064827595294526
[10]	Martin J C, Moyce W J.An experimental study of the collapse of liquid columns on a rigid horizontal plane[J].Philosophical Transactions of the Royal Society of London. Ser A, Mathematical and Physical Sciences,1952,244(882):312-324. doi: 10.1098/rsta.1952.0006

Relative Articles

[1]	MA Jinwei, DUAN Qinglin. Nearly Incompressible Elasto-Plastic Analysis of Extra-DOF-Free Generalized Finite Elements[J]. Applied Mathematics and Mechanics, 2024, 45(2): 220-226. doi: 10.21656/1000-0887.440067
[2]	LI Shuguang, QU Kai. Homogenization Modeling of Single-Phase Gas Local Flow in Porous Media[J]. Applied Mathematics and Mechanics, 2024, 45(2): 175-183. doi: 10.21656/1000-0887.440246
[3]	XU Yunqing, ZHOU Xiaomin, ZHAO Shiyi, XU Shengfei, SUN Zheng. Simulation Study on Dam Break Flow Based on the B-Spline Material Point Method[J]. Applied Mathematics and Mechanics, 2023, 44(8): 921-930. doi: 10.21656/1000-0887.430363
[4]	LI Nianbin, DONG Shiming, HUA Wen. Finite Element Analysis on Mixed-Mode Dynamic Fracture Experiments of Centrally Cracked Brazilian Disks With Crack Face Contact[J]. Applied Mathematics and Mechanics, 2021, 42(7): 704-712. doi: 10.21656/1000-0887.410349
[5]	CHEN Yafei, ZHENG Yunying. A Discontinuous Galerkin FEM for 2D Navier-Stokes Equations of Incompressible Viscous Fluids[J]. Applied Mathematics and Mechanics, 2020, 41(8): 844-852. doi: 10.21656/1000-0887.400379
[6]	WU Feng, SUN Yan, ZHONG Wan-xie. Inter-Belt Finite Element for the Analysis of Incompressible Material Problems[J]. Applied Mathematics and Mechanics, 2013, 34(1): 1-9. doi: 10.3879/j.issn.1000-0887.2013.01.001
[7]	S.Tariverdilo, J.Mirzapour, M.Shahmardani, Gh.Rezazadeh. Free Vibration of Membrane/Bounded Incompressible Fluid[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1091-1101. doi: 10.3879/j.issn.1000-0887.2012.09.006
[8]	ZHANG Yun-zhang, HOU Yan-ren, WEI Hong-bo. Adaptive Mixed Least Squares Galerkin/Petrov Finite Element Method for the Stationary Conduction Convection Problems[J]. Applied Mathematics and Mechanics, 2011, 32(10): 1182-1198. doi: 10.3879/j.issn.1000-0887.2011.10.005
[9]	LUO Yan, FENG Min-fu. Discontinuous Element Pressure Gradient Stabilizations for the Compressible Navier-Stokes Equations Based on Local Projections[J]. Applied Mathematics and Mechanics, 2008, 29(2): 157-168.
[10]	LUO Zhen-dong, MAO Yun-kui, ZHU Jiang. Petrov-Galerkin Least Squares Mixed Element Method for the Stationary Incompressible Magnetohydrodynamics[J]. Applied Mathematics and Mechanics, 2007, 28(3): 359-368.
[11]	Gu Haiming, Yang Danping, Sui Shulin, Liu Xinmin. Least-Squares Mixed Finite Element Method for a Class of Stokes Equation[J]. Applied Mathematics and Mechanics, 2000, 21(5): 501-510.
[12]	YAN Bo, ZHANG Ru-qing. Penalty Finite Element Method for Nonlinear Dynamic Response of Viscous Fluid-Saturated Biphasic Porous Media[J]. Applied Mathematics and Mechanics, 2000, 21(12): 1247-1254.
[13]	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.
[14]	Lu Dongqiang, Dai Shiqiang, Zhang Baoshan. Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System[J]. Applied Mathematics and Mechanics, 1999, 20(4): 331-336.
[15]	Guo Ben-yu, Cao Wei-ming. Spectral-Finite Element Method for Compressible Fluid Flow[J]. Applied Mathematics and Mechanics, 1992, 13(8): 677-692.
[16]	Chen Da-peng, Zhao Zhong. A Weighted Penalty Finite Element Method for the Analysis of Power-Law Fluid Flow Problems[J]. Applied Mathematics and Mechanics, 1990, 11(4): 279-282.
[17]	Chen Yao-song, Cao Nian-zheng. A Hybrid FEM Algorithm for Fluid Flow in a Visco-Elastic Pipe[J]. Applied Mathematics and Mechanics, 1989, 10(6): 517-622.
[18]	Lia Tong-ji, Pu Qun. An Exact Solution for Incompressible Flow Through a Two-Dimensional Laval Nozzle[J]. Applied Mathematics and Mechanics, 1986, 7(6): 487-495.
[19]	Su Ming-de. Finite Element Analysis of Non-Newtonian Fluid Flow in 2-D Branching Channel[J]. Applied Mathematics and Mechanics, 1986, 7(10): 929-936.
[20]	Li Yong-chi, T. C. T. Ting. Lagrangian Description of Transport Equations for Shock Waves in Three-Dimensional Elastic Solids[J]. Applied Mathematics and Mechanics, 1982, 3(4): 449-462.