Overlapping control volume approach for convection-diffusion problems

International Journal for Numerical Methods in Fluids

Volumn 23, Issue 9, 1996, Pages 865-882

  Verma, Atul Kumar ^a   Eswaran, V ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Convection diffusion; Finite volume method; Numerical diffusion; Overlapping control volume; Structured non orthogonal grid

Indexed keywords

DIFFUSION IN LIQUIDS; EQUATIONS OF MOTION; HEAT CONVECTION; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

FIVE POINT DIFFUSION MODELLING; ISOPARAMETRIC FORMULATION; OVERLAPPING CONTROL VOLUME; STRUCTURED NONORTHOGONAL GRIDS;

FINITE VOLUME METHOD;

EID: 0030291733     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0363(19961115)23:9<865::AID-FLD453>3.0.CO;2-3     Document Type: Article

References (24)

1. S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980.
2. D. B. Spalding, 'A novel finite-difference formulation for differential expressions involving both first and second derivatives', Int. j. numer. methods eng., 4, 551-559 (1972).
3. A. K. Runchal, 'Convergence and accuracy of three finite differences schemes for a two-dimensional conduction and convection problem', Int. j. numer. methods eng., 4, 541-550 (1972).
4. G. D. Raithby, 'A critical evaluation of upstream differencing applied to problems involving fluid flow', Comput. Methods Appl. Mech. Eng., 9, 75-103 (1976).
5. G. D. Raithby, 'Skew upstream differencing schemes for problems involving fluid flow', Comput. Methods Appl. Mech. Eng., 9, 153-164 (1976).
6. B. P. Leonard, 'A stable and accurate convective modelling procedure based on quadratic upstream interpolation', Comput. Methods Appl. Mech. Eng., 19, 59-98 (1979).
7. G. de Vahl Davis and G. D. Mallinson, 'An evaluation of upwind and central difference approximations by study of recirculating flows', Comput. Fluids, 4, 29-43 (1976).
8. T. Han, J. A. C. Humphrey and B. E. Launder, 'A comparison of hybrid and quadratic upstream differencing in high Reynolds number elliptic flows', Comput. Methods Appl. Mech. Eng., 29, 81-95 (1981).
9. A. Pollard and L. W. A. Siu, 'The calculations of some laminar flows using various discretization schemes', Comput. Methods Appl. Mech. Eng., 35, 293-313 (1982).
10. W. Shyy, 'Determination of relaxation factors for high cell Peclet number flow situation', Comput. Methods Appl. Mech. Eng., 43, 221-230 (1984).
11. C. M. Rhie and W. L. Chow, 'Numerical study of the turbulent flow past an airfoil with trailing edge separation', AIAA J., 21, 1525-1532 (1983).
12. C. F. Hsu, 'A curvilinear coordinate method for momentum heat and mass transfer in domains of irregular geometry', Ph.D. Thesis, University of Minnesota, 1981.
13. C. M. Rhie, 'A numerical study of flow past an isolated airfoil with separation', Ph.D. Thesis, University of Illinois at Urbana-Champaign, 1981.
14. M. Peric, 'A finite volume method for prediction of three dimensional fluid flow in complex ducts', Ph.D. Thesis, Univ of London, 1985.
15. A. Mukhopadhyay, T. Sundararajan and G. Biswas, 'An explicit transient algorithm for predicting incompressible flows in arbitrary geometry', Int. j. numer. methods fluids, 17, 975-993 (1993).
16. Y.-H. Hwang, 'Arbitrary domain velocity analyses for the incompressible Navier-Stokes equations', J. Comput. Phys., 110, 134-139 (1994).
17. B. R. Baliga and S. V. Patankar, 'A new finite element formulation for convection-diffusion problems', Numer. Heat Transfer, 3, 393-410 (1980).
18. B. LeDain-Muir and B. R. Baliga, 'Solution of three-dimensional convection-diffusion problems using tetrahedral elements and flow-oriented upwind interpolation functions', Numer. Heat Transfer, 9, 253-276 (1986).
19. S. Ramadhyani and S. V. Patankar, 'Solution of the convection diffusion equation by a finite-element method using quadrilateral elements', Numer. Heat Transfer, 8, 595-612 (1985).
20. G. E. Schneider and M. J. Raw, 'A skewed positive influence coefficient upwinding procedure for control volume base finite element convection-diffusion computation', Numer. Heat Transfer, 9, 1-26 (1986).
21. C. Hirsch, Numerical Computation of Internal and External Flows, Vol. I, Wiley, New York, 1988.
22. A. A. Amsden, J. D. Ramshaw, P. J. O'Rouke and J. K. Dukowicz, 'KIVA: a computer program for two- and three-dimensional fluid flows with chemical reactions and fuel sprays', LA-10245-MS, 1985 (unpublished).
23. B. P. Leonard and J. E. Drummond, 'Why you should not use hybrid, power-law or related exponential schemes for convection-modelling - there are much better alternatives', Int. j. numer. methods fluids, 20, 421-442 (1995).
24. S. Majumdar, W. Rodi and J. Zhu, 'Three-dimensional finite-volume method for incompressible flows with complex boundaries', Trans. ASME, 114, 496-503 (1992).