THE CONJUGATE GRADIENT METHOD AND BLOCK ITERATIVE METHOD FOR PENALTY FINITE ELEMENT OF THREE DIMENSIONAL NAVIER-STOKES EQUATION

Abstract

Abstract: A conjugate gradient and block iterative algorithm for element solution of penalty variational form of Navier-Stokes equations are presented. Because the algorithm of solving single variable minimizing problem is simplified, the computing time is greatly saved.In this paper numerical examples are also provided.

Key words: largeeddy simlation (LES), turbulent mixing zone (TMZ), validation, interface instability, multi-viscous-fluid and turbulence (MVFT)

Li Kai-tai;Huang Ai-xiang;Li Du;Liu Zhi-xing. THE CONJUGATE GRADIENT METHOD AND BLOCK ITERATIVE METHOD FOR PENALTY FINITE ELEMENT OF THREE DIMENSIONAL NAVIER-STOKES EQUATION. Applied Mathematics and Mechanics (English Edition), 1983, 4(6): 927-941.

TrendMD

References

[1] Li Kai-tai,Huang Ai-xiang,Ma Yi-chen,Li Du and Liu Zhi-xiang,Optimal control finite element approximation for penalty variational formulatio of the Navier-Stokes problem,J.Xian Jiaotong University,Vol.16,No.1,85-88,(1982).(in Chinese) .
[2] Li Du,Conjugate gradient algorithm and numerical experimentation for three-dimensional Navier-Stokes problem,J.Xian Jiaotong University,Vol.16,No.4,81-90,(1982).(in Chinese) .
[3] Liu Zhi-xiang,The block iteration method and the program for penalty variational form of three-dimensional Navier-Stokes problems,J.Xian Jiaotong University,Vol.16,No.4,91-102,(1982).(in Chinese) .
[4] Bristeau,M.O.,O.Pironneau,R.Glowinski,J.Periaux and P.Perrier,On the numerical solution of nonlinear problems in fluid dynamics by least squares and finite element methods (I):Least square formulation and conjugate gradient solution of the continuous problems,Comp.Math.Appl.Mech.Eng.(17) /(18),(1979),619-657. .
[5] Giraut,V.,and P.A.Raviart,Finite Element Approximation for the Navier-Stokes Equations,Lecture Notes in Mathematics,Vol.749,Springer-Verlag,Berlin,(1980). .
[6] Teman,R.,Navier-Stokes Equations,North-Holland,Amsterdam,(1977). .
[7] Reddy,J.N.,On the Mathematical Theory of the Penalty-Finite Elements for Navier-Stokes Equations,Proceedings of the Third International Conference onFinite Elements in Flow Problems,Vol.2,(1980) .
[8] Zienkiewicz,O.C.,Constrained Variational Principles and Penalty Function Methods in Finite Element Analysis,Lecture Notes in Mathematics,P.363(Edited by Dald and B.B.Eckman),Springer-Verlag,New York,(1974). .
[9] Falk,R.S.,and J.T.King,A penalty and extrapolation method for the stationary Stokes equations,SIAM.J.Numer.Anal 13(1979),814-829. .
[10] Bercoviex,M.,and M.Engelman,A finite element for the numerical solution of viscous incompressible flows,J.Comp.Phys.30(1979),181-201. .
[11] Hughes,T.J.R.,W.K.Liu and A.Brooks,Finite element analysis of incompressible viscous flows by the penalty function formulation,J.Comp.Phys.,30(1979) 1-60. .
[12] Song,Y.J.,J,T.Oden and N.Kikuchi,Discrete LBB-Conditions for RIP-Finite Element Methods,TICON Report,80-7(1980). .
[13] Oden,J.T.,RIP-Methods for Stokesian Flows,Finite Elements in Fluids,Vol.4,John Wiley Sons. .
[14] Oden,J.T.,Penalty Methods and Selective Reduced Integration for Stokesian Flow,Proceedings of the Third International Conference on Finite Elements in Flow Problems,Banff.Alberta,Canada,(1980),140-145. .
[15] Oden,J.T.,Penalty Finite Element Methods for Constrained Problems in Elasticity,Symposium on Finite Element Methods,held in Hefei,Anhui Province,The People‘s Republic of China,(1981).