Fourier analysis of the simple algorithm formulated on a collocated grid

Numerical Heat Transfer, Part B: Fundamentals

Volumn 30, Issue 1, 1996, Pages 45-66

  Miller, Timothy F ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; HEAT TRANSFER; ITERATIVE METHODS; NAVIER STOKES EQUATIONS; PRESSURE EFFECTS;

COLLOCATED GRID; CONVERGENCE OF THE COLLOCATED FORM; FOURIER ANALYSIS; FOURIER ERROR AMPLIFICATION MATRIX; MOMENTUM UNDERRELAXATION FACTOR; PRESSURE CORRECTION DAMPING FACTOR; RHIE-CHOW APPROXIMATION; SIMPLE ALGORITHM;

FOURIER TRANSFORMS;

EID: 0030196084     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/10407799608915071     Document Type: Article

References (15)

1. S. V. Patankar and D. B. Spalding, A Calculation Procedure for Heat and Mass Transfer in 3-D Parabolic Flows, Int. J. Heat Mass Transfer, vol. 15, pp. 1787-1806, 1972.
2. S. V. Patankar, A Calculational Procedure for Two-Dimensional Elliptic Situations, Numer. Heat Transfer, vol. 4, pp. 409-425, 1981.
3. R. Issa, Solution of the Implicitly Discretized Fluid Flow Equations by Operator Splitting, J. Comput. Phys., vol. 62, pp. 40-65, 1986.
4. J. P. Van Doormaal and G. D. Raithby, Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flows, Numer. Heat Transfer, vol. 7, pp. 147-163, 1984.
5. G. J. Shaw and S. Sivaloganathan, On the Smoothing Properties of the SIMPLE Pressure-Correction Algorithm, Int. J. Numer. Meth. Fluids, vol. 8, pp. 441-461, 1988.
6. S. Sivaloganathan and G. J. Shaw, A Multigrid Method for Recirculating Flows, Int. J. Numer. Meth. Fluids, vol. 8, pp. 417-440, 1987.
7. C. M. Rhie and W. L. Chow, A Numerical Study of the Turbulent Flow Past an Isolated Airfoil with Trailing Edge Separation, AIAA J., vol. 21, pp. 1525-1532, 1983.
8. T. F. Miller and F. W. Schmidt, Use of a Pressure-Weighted Interpolation Method for the Solution of the Incompressible Navier-Stokes Equations on a Nonstaggered Grid System, Numer. Heat Transfer, vol. 14, pp. 213-233, 1988.
9. G. D. Raithby and G. E. Schneider, Numerical Solution of Problems in Incompressible Fluid Flow: Treatment of the Velocity-Pressure Coupling, Numer. Heat Transfer, vol. 2, pp. 417-440, 1979.
10. C. M. Rhie, A Pressure Based Navier-Stokes Solver Using the Multigrid Method, A1AA-86-0207, 24th Aerospace Sciences Meeting, Reno, NV, 1986.
11. M. Peric, R. Kessler, and G. Scheuerer, Comparison of Finite-Volume Numerical Methods with Staggered and Collocated Grids, Comput. Fluids, vol. 16, pp. 389-403, 1988.
12. M. Barcus, M. Peric, and G. Scheuerer, A Control Volume Based Full Multigrid Procedure for the Prediction of Two-Dimensional Laminar Incompressible Flows, in Notes on Numerical Fluid Mechanics, vol. 20, pp. 9-16, Vieweg Verlag, Braunschweig, 1988.
13. C. Becker, J. H. Ferziger, M. Peric, and G. Sheuerer, Finite Volume Multigrid Solutions of the Two-Dimensional Incompressible Navier-Stokes Equations, in Notes on Numerical Fluid Mechanics, vol. 22, pp. 30-40, Vieweg Verlag, Braunschweig, 1989.
14. R. E. Phillips and F. W. Schmidt, A Multilevel-Multigrid Technique for Recirculating Flows, Numer. Heat Transfer, vol. 8, pp. 573-594, 1985.
15. T. F. Miller and F. W. Schmidt, Evaluation of a Multilevel Technique Applied to the Poisson and Navier-Stokes Equations, Numer. Heat Transfer, vol. 13, pp. 1-19, 1988.