Solution of the Div-Curl Problem in Generalized Curvilinear Coordinates

Journal of Computational Physics

Volumn 138, Issue 1, 1997, Pages 121-152

  Bertagnolio, F ^a   Daube, O ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CURVILINEAR GRIDS; DIFFERENTIAL OPERATORS; DISCRETE PROBLEMS; GENERALIZED CURVILINEAR COORDINATES; HELMHOLTZ; MAC SCHEMES; MACHINE ACCURACY; NON-ORTHOGONAL; VECTOR ANALYSIS; VECTOR FIELDS;

MATHEMATICAL OPERATORS;

EID: 0001465138     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5800     Document Type: Article

References (23)

1. Apanovich Y. V., Lyumkis E. D. Difference schemes for the Navier-Stokes equations on a net consisting of Dirichlet cells. U.S.S.R. Comput. Maths. Math. Phys. 28:1988;57.
2. Aris R. Vectors, Tensors and the Basic Equations of Fluid Mechanics. 1962;Prentice Hall, Englewood Cliffs.
3. Bernard R. S., Kapitza H. How to discretize the pressure gradient for curvilinear MAC grids. J. Comput. Phys. 99:1992;288.
4. F. Bertagnolio, O. Daube, 1996, Velocity-vorticity formulation of the incompressible Navier-Stokes equations on nonorthogonal grids, Proceedings of the Third ECCOMAS Computational Fluid Dynamics Conference, Paris, France, 1996, 644.
5. Daube O. Resolution of the 2D Navier-Stokes equations in velocity-vorticity form by means of an influence matrix. J. Comput. Phys. 103:1992;402.
6. Demirdzic I., Gosman A. D., Issa R. I., Peric M. A calculation procedure for turbulent flow in complex geometries. Comput. & Fluids. 15:1987;251.
7. Favorskii A., Samarskii A., Shashkov M., Tishkin V. Operational finite-difference schemes. Differential Equations. 17:1981;854.
8. Gatski T. B. Review of incompressible fluid flow computations using the vorticity-velocity formulation. Appl. Numer. Math. 7:1991;227.
9. Gatski T. B., Grosch C. E., Rose M. E. A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables. J. Comput. Phys. 48:1982;1.
10. Girault V., Raviart P. A. Finite Element Methods for Navier-Stokes Equations. 1986;Springer-Verlag, Berlin/New York.
11. Harlow R. S., Welch J. E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids. 8:1965;2182.
12. Huang Y., Ghia U. A multigrid method for solution of vorticity-velocity form of 3-D Navier-Stokes equations. Commun. Appl. Numer. Methods. 8:1992;707.
13. K. C. Karki, 1986, A Calculation Procedure for Viscous Flows at all Speeds in Complex Geometries, University of Minnesota.
14. Knorr G., Joyce G., Marcus A. J. J. Comput. Phys. 38:1980;227.
15. Nicolaides R. A. Direct Discretisation of Planar Div-Curl Problems. ICASE Report. 89-76:1989.
16. Osswald G. A., Ghia K. N., Ghia U. A direct algorithm for solution of incompressible three-dimensional unsteady Navier-Stokes equations. AIAA Paper. 87-1139:1987;408.
17. Pascazio G., Napolitano M. A staggered-grid finite volume method for the vorticity-velocity equations. Comput. & Fluids. 25:1996.
18. Quartapelle L. Numerical Solution of the Incompressible Navier-Stokes Equations. International Series of Numerical Mathematics. 113:1993;Birkhäuser, Basel.
19. Rosenfeld M., Kwak D., Vinokur M. A solution method for the unsteady and incompressible Navier-Stokes equations in generalized coordinate systems. AIAA Paper. 88-0718:January, 1988.
20. Shashkov M., Steinberg S. Support-operator finite-difference algorithms for general elliptic problems. J. Comput. Phys. 118:1995;131.
21. Shyy W., Vu T. C. On the adoption of velocity variable and grid system for fluid flow computation in curvilinear coordinates. J. Comput. Phys. 92:1991;82.
22. Strikwerda J. C. Finite Difference Schemes and Partial Differential Equations. 1989;Chapman & Hall, London/New York.
23. Yang H. Q., Habchi S. D., Przekwas A. J. General strong conservation formulation of Navier-Stokes equations in nonorthogonal curvilinear coordinates. AIAA J. 32:1994;936.