A transformation-free HOC scheme for steady convection-diffusion on non-uniform grids

International Journal for Numerical Methods in Fluids

Volumn 44, Issue 1, 2004, Pages 33-53

  Kalita, Jiten C ^a   Dass, Anoop K ^b   Dalal, D C ^b  

^a GEORGE WASHINGTON UNIVERSITY   (United States)

^b INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI   (India)

Author keywords

Convection diffusion; Efficient; High Re; HOC; Non uniform; Resolution

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DIFFUSION; FINITE DIFFERENCE METHOD; MATRIX ALGEBRA; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER;

TRANSFORMATION TECHNIQUES;

FLOW OF FLUIDS;

COMPUTATIONAL FLUID DYNAMICS; CONVECTION-DIFFUSION EQUATION; MATHEMATICAL METHOD;

EID: 0345761443     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.621     Document Type: Article

References (23)

1. Anderson DA, Tannehil JC, Pletcher RH. Computational Fluid Mechanics and Heat Transfer. Hemisphere Publishing Corporation: New York, 1984.
2. Anderson Jr JD. Computational Fluid Dynamics. McGraw-Hill, Inc.: New York, 1993.
3. Hoffman JD. Numerical Methods for Engineers and Scientists. McGraw-Hill, Inc.: Singapore, 1993.
4. Noye BJ, Tan HH. Finite difference methods for solving two-dimensional advection diffusion equation. International Journal for Numerical Methods in Fluids 1989; 9:75-98.
5. Spotz WF, Carey GF. High-order compact scheme for the steady stream-function vorticity equations. International Journal for Numerical Methods in Engineering 1995; 38:3497-3512.
6. Mackinnon RJ, Johnson RW. Differential equation based representation of truncation errors for accurate numerical solution. International Journal for Numerical Methods in Fluids 1991; 13:739-757.
7. Strikwerda JC. High-order accurate schemes for incompressible viscous flow. International Journal for Numerical Methods in Fluids 1997; 24:715-734.
8. Yanwen M, Dexun F, Kobayashi T, Taniguchi N. Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme. International Journal for Numerical Methods in Fluids 1999; 30:509-521.
9. Kalita JC, Dalal DC, Dass AK. A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equations with variable convection coefficients. International Journal for Numerical Methods in Fluids 2002; 38:1111-1131.
10. Kalita JC. HOC schemes for incompressible viscous flows: application and development. PhD Thesis, Indian Institute of Technology Guwahati, May, 2002.
11. Li M, Tang T, Fornberg B. A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1995; 20:1137-1151.
12. Gupta MM. High accuracy solutions of incompressible Navier-Stokes equations. Journal of Computational Physics 1991; 93: 343-359.
13. Kalita JC, Dalal DC, Dass AK. Fully compact higher order computation of steady state natural convection in a square cavity. Physical Review E 2001; 64(6):066703 (1-13).
14. Spotz WF, Carey GF. Formulation and experiments with high-order compact schemes for nonuniform grids. International Journal for Numerical Methods in Heat and Fluid Flow 1998; 8(3):288-303.
15. Zhang J, Lixin GE, Gupta MM. Fourth order compact difference scheme for 3D convection-diffusion equation with boundary layers on nonuniform grids. Neural, Parallel and Scientific Computing 2000; 8:373-392.
16. Sleijpen GLG, van der Vorst HA. Hybrid bi-conjugate gradient methods for CFD problems. In Computational Fluid Dynamics Review, Hafez M, Oshima K (eds). Wiley: Chichester, 1995; 457-476.
17. Gartland Jr. EC. Discrete weighted mean approximation of a model convection-diffusion equation. SIAM Journal on Scientific and Statistical Computing 1995; 3:460-472.
18. Gupta MM, Manohar RM, Stephenson JH. A single cell high order scheme for the convection-diffusion equation with variable coefficients. International Journal for Numerical Methods in Fluids 1984; 4:641-651.
19. Janssen RJA, Henkes RAWM. Accuracy of finite volume discretizations for bifurcating natural convection in a square cavity. Numerical Heat Transfer 1993; 24:191-207.
20. Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equation and a multigrid method. Journal of Computational Physics 1982; 48:387-411.
21. Kim J, Moin P. Application of fractional step method to incompressible Navier-Stokes equations. Journal of Computational Physics 1985; 59:308-323.
22. Schreiber R, Keller HB. Driven cavity flow by efficient numerical techniques. Journal of Computational Physics 1983; 49:310-333.
23. Bruneau C-H, Jouron C. An efficient scheme for solving steady incompressible Navier-Stokes equations. Journal of Computational Physics 1990; 89:389-413.