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Journal of Zhejiang University SCIENCE A 2011 Vol.12 No.1 P.33-45

http://doi.org/10.1631/jzus.A1000098


A semi-implicit three-step method based on SUPG finite element formulation for flow in lid driven cavities with different geometries


Author(s):  Cheng Huang, Dai Zhou, Yan Bao

Affiliation(s):  School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Corresponding email(s):   ryanhuang@sjtu.edu.cn, zhoudai@sjtu.edu.cn, ybao@sjtu.edu.cn

Key Words:  Semi-implicit three-step method, Streamline upwind/Petrov-Galerkin (SUPG) finite element method (FEM), Unsteady incompressible flows, Lid driven cavity problem


Cheng Huang, Dai Zhou, Yan Bao. A semi-implicit three-step method based on SUPG finite element formulation for flow in lid driven cavities with different geometries[J]. Journal of Zhejiang University Science A, 2011, 12(1): 33-45.

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author="Cheng Huang, Dai Zhou, Yan Bao",
journal="Journal of Zhejiang University Science A",
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pages="33-45",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1000098"
}

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%T A semi-implicit three-step method based on SUPG finite element formulation for flow in lid driven cavities with different geometries
%A Cheng Huang
%A Dai Zhou
%A Yan Bao
%J Journal of Zhejiang University SCIENCE A
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%P 33-45
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%D 2011
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1000098

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T1 - A semi-implicit three-step method based on SUPG finite element formulation for flow in lid driven cavities with different geometries
A1 - Cheng Huang
A1 - Dai Zhou
A1 - Yan Bao
J0 - Journal of Zhejiang University Science A
VL - 12
IS - 1
SP - 33
EP - 45
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Y1 - 2011
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A1000098


Abstract: 
A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Bao, Y., Zhou, D., Zhao, Y.Z., 2010a. A two-step taylor-characteristic-based Galerkin method forincompressible flows and its application to flow over triangular cylinder with different incidence angles. International Journal for Numerical Methods in Fluids, 62(11):1181-1208.

[2]Bao, Y., Zhou, D., Huang, C., 2010b. Numerical simulation of flow over three circular cylinders in equilateral arrangements at low Reynolds number by a second-order characteristic-based split finite element method. Computers & Fluids, 39(5):882-899.

[3]Belytschko, T.B., Liu, W.K., Moran, B., 2000. Nonlinear Finite Elements for Continua and Structures. Wiley, Chichester.

[4]Brezzi, F., Bristeau, M.O., Franca, L.P., Mallet, M., Roge, G., 1992. A relationship between stabilized finite element methods and the Galerkin method with bubble functions. Computer Methods in Applied Mechanics and Engineering, 96(1):117-129.

[5]Brooks, A.N., Hughes, T.J.R., 1982. Streamline upwind/ Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 32(1-3):199-259.

[6]Demirdžić, I., Lilek, Ž., Perić, M., 1992. Fluid flow and heat transfer test problems for non-orthogonal grids: benchmark solutions. International Journal for Numerical Methods in Fluids, 15(3):329-354.

[7]Dettmer, W., Perić, D., 2006a. A computational framework for fluid-rigid body interaction: Finite element formulation and applications. Computer Methods in Applied Mechanics and Engineering, 195(13-16):1633-1666.

[8]Dettmer, W., Perić, D., 2006b. A computational framework for free surface fluid flows accounting for surface tension. Computer Methods in Applied Mechanics and Engineering, 195(23-24):3038-3071.

[9]Dettmer, W., Perić, D., 2006c. A computational framework for fluid-structure interaction: Finite element formulation and applications. Computer Methods in Applied Mechanics and Engineering, 195(41-43):5754-5779.

[10]Donea, J., Giuliani, S., Laval, H., Quartapelle, L., 1984. Time-accurate solution of advection-diffusion problems by finite elements. Computer Methods in Applied Mechanics and Engineering, 45(1-3):123-145.

[11]Franca, L.P., Frey, S.L., 1992. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 99(2-3):209-233.

[12]Ghia, U., Ghia, K.N., Shin, C.T., 1982. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of ComputationalPhysics, 48(3):387-411.

[13]Hughes, T.J.R., 1995. Multiscale phenomena: Greens functions subgrid scale models, bubbles and the origins of stabilized methods. Computer Methods in Applied Mechanics and Engineering, 127(1-4):387-401.

[14]Hughes, T.J.R., Tezduyar, T.E., 1984. Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Computer Methods in Applied Mechanics and Engineering, 45(1-3):217-284.

[15]Hughes, T.J.R., Franca, L.P., Balestra, M., 1986. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering, 59(1):85-99.

[16]Hughes, T.J.R., Franca, L.P., Hulbert G.M., 1989. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations. Computer Methods in Applied Mechanics and Engineering, 73(2):173-189.

[17]Jiang, C.B., Kawahara, M., 1993. A three step finite element method for unsteady incompressible flows. Computational Mechanics, 11(5-6):355-370.

[18]Jyotsna, R., Vanka, S.P., 1995. Multigrid calculation of steady, viscous flow in a triangular cavity. Journal of Computational Physics, 122(1):107-117.

[19]Kjellgren, P., 1997. A semi-implicit fractional step finite element method for viscous incompressible flows. Computational Mechanics, 20(6):541-550.

[20]Kohno, H., Bathe, K.J., 2006. A flow-condition-based interpolation finite element procedure for triangular grids. International Journal for Numerical Methods in Fluids, 51(6):673-699.

[21]Oñate, E., 1998. Derivation of stabilized equations for advective-diffusive transport and fluid flow problems. Computer Methods in Applied Mechanics and Engineering, 151(1-2):233-267.

[22]Oñate, E., Valls, A., Garcia, J., 2007. Modeling incompressible flows at low and high Reynolds numbers via a finite calculus-finite element approach. Journal of Computational Physics, 224(1):332-351.

[23]Ribbens, C.J., Watson, L.T., 1994. Steady viscous flow in a triangular cavity. Journal of Computational Physics, 112(1):173-181.

[24]Selmin, V., Donea, J., Quartapelle, L., 1985. Finite element methods for nonlinear advection. Computer Methods in Applied Mechanics and Engineering, 52(1-3):817-845.

[25]Tezduyar, T.E., 2007a. Finite elements in fluids: Stabilized formulations and moving boundaries and interfaces. Computers & Fluids, 36(2):191-206.

[26]Tezduyar, T.E., 2007b. Finite elements in fluids: Special methods and enhanced solution techniques. Computers & Fluids, 36(2):207-223.

[27]Tezduyar, T.E., Ganjoo, D.K., 1986. Petrov-Galerkin formulations with weighting functions dependent upon spatial and temporal discretization: Applications to transient convection-diffusion problems. Computer Methods in Applied Mechanics and Engineering, 59(1):49-71.

[28]Zienkiewicz, O.C., Codina, R., 1995. A general algorithm for compressible and incompressible flow. Part I: The split characteristic based scheme. International Journal for Numerical Methods in Fluids, 20(8-9):869-885.

[29]Zienkiewicz, O.C., Morgan, K., Satya Sai, B.V.K., Codina, R., Vazquez, M., 1995. A general algorithm for compressible and incompressible flow. Part II: Tests on the explicit form. International Journal for Numerical Methods in Fluids, 20(8-9):887-913.

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