A Penalty-Hybrid Finite Element Analysis of Stokes Flow

Chen Da-peng; Zhao Zhong

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1990 > 11(6): 467-476

Chen Da-peng, Zhao Zhong. A Penalty-Hybrid Finite Element Analysis of Stokes Flow[J]. Applied Mathematics and Mechanics, 1990, 11(6): 467-476.

Citation:

Chen Da-peng, Zhao Zhong. A Penalty-Hybrid Finite Element Analysis of Stokes Flow[J]. Applied Mathematics and Mechanics, 1990, 11(6): 467-476.

Citation:

Chen Da-peng, Zhao Zhong. A Penalty-Hybrid Finite Element Analysis of Stokes Flow[J]. Applied Mathematics and Mechanics, 1990, 11(6): 467-476.

PDF( 615 KB)

A Penalty-Hybrid Finite Element Analysis of Stokes Flow

Southwest Jiaotong University, Chengdu

Received Date: 1989-06-19
Publish Date: 1990-06-15

Abstract

Abstract

A type of penalty-hybrid variational principle is suggested for the analysis of Stokesian flow. On such a basis, a finite element model is formulated featuring, among others, a priori satisfaction of the deviatoric stress and hydrostatic pressure on linear momentum balance equations. Also in the present scheme the hydrostatic pressure is successfully eliminated at the element level, leaving only nodal velocities as solution unknowns. A series of 4-node and 8-node quadrilateral elements are derived and examined. Numerical examples demonstrating their characteristic behaviors are also included.

FullText(HTML)

References(16)

References

[1]	Olson,M.D.,A variational finite element method for two-dimensional steady,viscous flows,Proc.Special Conf.F.E.M.in Civil Eng.,Engineering Institute of Canada(1972),585-616.
[2]	Cheng,R.T.,Numerical solution of the Navier-Stokes equations by the finite elementmethod,Phys.of Fluids,15(1972),2098-2105.
[3]	Taylor,C.and P.Hood,A numerical solution of the Navier-Stokes equations using the finiteelement technique,Compt.Fluids,1(1973),73-100.
[4]	Oden,J.T.and L.C.Wellford,Analysis of flow of viscous fluids by the finite element method,AIAA J.,10(1972),1590-1599.
[5]	Babuška,I.,Error bounds for finite element method,Numer.Math.,16(1971),322-333.
[6]	Brezzi,F.,On the existence,uniqueness and approximation of saddle point problems arising from Lagrange multipliers,R.A.I.R.O.,Série,R2(1974),129-151.
[7]	Sani,R.L.,P.M.Gresho and R.L.Lee,On the spurious pressure generated by certain GFEM solutions of the incompressible Navier-Stokes equations,3rd.Int.Conf.on F.E.in Flow Problems,Banff,Canada(1980).
[8]	Hughes,T.J.R.,W.K.Liu and A.Brooks,Finite element analysis of incompressible viscous flow by the penalty function formulations,J.Compt.Phys.,30(1979),1-60.
[9]	Bercovier,M.and M.Engelman,A finite element for the numerical solution of viscous incompressible flow,J.Compt.Phys.,30(1979),181-201.
[10]	Oden,J.T.,N.Kikuchi and S.W.Song,Penalty-finite element methods for the analysis of Stokesian flows,Compt.Meth.Appl.Mech.Eng.,31(1982),297-327.
[11]	Oden,J.T.,Penalty method and reduced integration for the analysis of fluids,Penalty-Finite Element Methods in Mechanics,AMD-51,Ed.J.N.Reddy(1982),21-32.
[12]	Carey,G.F.and R.Krishnan,Penalty approximations of Stokes flow,Compt.Meth.Appl.Mech.Eng.,35(1982),169-206.
[13]	Bratianu,C.and S.N.Atluri,A hybrid finite element method for Stokes flow:Part I-Formulation and numerical studies,Compt.Meth.Appl.Mech.Eng.,36(1983),23-37.
[14]	Ying,L.A.and S.N.Atluri,A hybrid finite element method for Stokes flow:part Ⅱ-Stability and convergence studies,Compt.Meth.Appl.Mech.Eng.,36(1983),39-60.
[15]	应隆安,粘性不可压缩流体运动的有限元法,数学进展,12 (1983), 124-132.
[16]	Schlichting,H.,Boundary-Layer Theory,6th edition,McGraw-Hill,New York(1968).