Numerical Solution of the Incompressible Navier-Stokes Equations with Coriolis Forces Based on the Discretization of the Total Time Derivative

Journal of Computational Physics

Volumn 148, Issue 2, 1999, Pages 467-496

  Codina, Ramon ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Coriolis forces; Incompressible flows; Inertial bases; Method of characteristics; Stabilized finite element methods

Indexed keywords

FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; REYNOLDS NUMBER; VISCOUS FLOW;

DISCRETIZATIONS; FRAMES OF REFERENCE; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; INERTIAL BASE; METHOD OF CHARACTERISTICS; ROTATING FRAME; STABILIZED FINITE ELEMENT; STABILIZED FINITE ELEMENT METHOD; TIME DERIVATIVE;

CORIOLIS FORCE;

EID: 0000997097     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6126     Document Type: Article

References (18)

1. Douglas J., Russell T. F. Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal. 19:1982;871.
2. Pironneau O. On the transport-diffusion algorithm and its applications to the Navier-Stokes equations. Numer. Math. 38:1982;309.
3. Löhner R., Morgan K., Zienkiewicz O. C. The solution of non-linear hyperbolic equation systems by the finite element method. Int. J. Num. Meth. Fluids. 4:1984;1043.
4. Zienkiewicz O. C., Codina R. A general algorithm for compressible and incompressible flow. Part I. The split, characteristic based scheme. Int. J. Num. Meth. Fluids. 20:1995;869.
5. Brooks A. N., Hughes T. J. R. Streamline upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comp. Meth. Appl. Mech. Engng. 32:1982;199.
6. Hughes T. J. R., Franca L. P., Hulbert G. M. A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations. Comp. Meth. Appl. Mech. Engng. 73:1989;173.
7. Donea J. A Taylor-Galerkin method for convection transport problems. Int. J. Num. Meth. Engrg. 20:1984;101.
8. Codina R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Comp. Meth. Appl. Mech. Engng. 156:1998;185.
9. Heywood J. G., Rannacher R. Finite element approximation of the nonstationary Navier-Stokes problem. II. Stability of solutions and error estimates uniform in time. SIAM J. Numer. Anal. 23:1986;750.
10. Ladyzhenskaya O. The Mathematical Theory of Viscous Incompressible Flow. 1963.
11. Codina R., Soto O. Finite element solution of the Stokes problem with dominating Coriolis force. Comp. Meth. Appl. Mech. Engng. 142:1997;215.
12. Chorin A. J. Numerical solution of the Navier-Stokes equations. Math. Comput. 22:1968;745.
13. Temam R. Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionaires (I). Arch. Rat. Mech. Anal. 32:1969;135.
14. Blair Perot J. An analysis of the fractional step method. J. Comput. Phys. 108:1993;51.
15. Brezzi F., Fortin M. Mixed and Hybrid Finite Element Methods. 1991.
16. Hughes T. J. R., Liu W. K., Brooks A. Finite element analysis of incompressible viscous flows by the penalty function formulation. J. Comput. Phys. 30:1979;1.
17. Hughes T. J. R., Franca L. P., Balestra M. A new finite element formulation for computational fluid dynamics. V. Circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation for the Stokes problem accommodating equal-order interpolations. Comput. Meth. Appl. Mech. Engrg. 59:1986;85.
18. Tritton D. J. Physical Fluid Dynamics. 1977.