×

zbMATH — the first resource for mathematics

Finite volume methods for laminar and turbulent flows using a penalty function approach. (English) Zbl 0806.76066
A penalty function, finite volume method is described for two-dimensional laminar and turbulent flows. Turbulence is modelled using the \(k- \varepsilon\) model. The governing equations are discretized, and the resulting algebraic equations are solved using both sequential and coupled methods. The performance of these methods is gauged with reference to a tuned SIMPLE-C algorithm. Flows considered are a square cavity with a sliding top, a plane channel flow, a plane jet impingement and a plane channel with a sudden expansion.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
76F10 Shear flows and turbulence
Software:
ILUBCG2; YSMP
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Raithby, Numer Heat Transfer 2 pp 417– (1979)
[2] Latimer, Numer. Heat Transfer 8 pp 635– (1985)
[3] Patankar, Int. J. Heat Mass Transfer 15 pp 1787– (1972)
[4] Patankar, Numer. Heat Transfer 4 pp 409– (1981)
[5] Van Doormaal, Numer. Heat Transfer 7 pp 147– (1984)
[6] Vanka, Int. J. Heat Mass Transfer 28 pp 2093– (1985)
[7] Reddy, Int. j. numer. methods fluids 2 pp 151– (1985)
[8] Reddy, Comput. Methods Appl. Mech. Eng. 35 pp 87– (1985)
[9] Temam, Bull. Soc. Math. Fr. 96 pp 115– (1968)
[10] ’Development and evaluation of iterative and direct methods for the solution of the equations governing recirculating flows’, Ph.D Thesis, University of Minnesota, 1985.
[11] De Bremaecker, Comput. Fluids 15 pp 275– (1987)
[12] Chorin, J. Comput. Phys. 2 pp 12– (1967)
[13] Shih, Numer. Heat Transfer 15 pp 127– (1989)
[14] ’The numerical calculation of laminar and turbulent flows using penalty-function finite-volume methods’, Ph.D. Thesis, Department of Mechanical Engineering, Queen’s University at Kingston, 1990.
[15] Rogers, AIAA J. 28 pp 253– (1990)
[16] Hughes, J. Comput. Phys. 30 pp 1– (1979)
[17] Spalding, Int. j. numer. methods eng. 4 pp 551– (1972)
[18] Stone, SIAM J. Numer. Anal. 5 pp 530– (1968)
[19] Schneider, Numer. Heat Transfer 4 pp 1– (1981)
[20] Bertin, Numer. Heat Transfer 10 pp 311– (1986)
[21] D’Yakonov, Dokl. Akad. Nauk SSSR 138 pp 522– (1961)
[22] Koniges, Comput. Phys. Commun. 43 pp 297– (1987)
[23] , and , ’Yale Sparse Matrix Package I–The symmetric codes’, Rep. 112, Department of Computer Science, Yale University, 1977.
[24] , and , ’Yale Sparse Matrix Package II–The non-symmetric codes’, Rep. 114, Department of Computer Science, Yale University, 1977.
[25] and , ’Fully-coupled solution of pressure-linked fluid flow equations’, Rep. ANL-83-73, Argonne National Laboratory, University of Chicago, 1983.
[26] , and , Numerical Recipes–The Art of Scientific Computing, Cambridge University Press, Cambridge 1986. · Zbl 0587.65003
[27] Launder, Comput. Methods Appl. Mech. Eng. 3 pp 269– (1974)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.