Explicit and semi-implicit CBS procedures for incompressible viscous flows

International Journal for Numerical Methods in Engineering

Volumn 66, Issue 10, 2006, Pages 1618-1640

  Massarotti, N ^a   Arpino, F ^a   Lewis, R W ^b   Nithiarasu, P ^b  

^a UNIVERSITY OF CASSINO AND SOUTHERN LAZIO   (Italy)

^b SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

CBS; Explicit; Incompressible flow; Semi implicit

Indexed keywords

ALGORITHMS; COMPRESSIBILITY; INCOMPRESSIBLE FLOW; UNSTEADY FLOW;

CHARACTERISTIC-BASED SPLIT (CBS); EXPLICIT; SEMI-IMPLICIT;

VISCOUS FLOW;

ALGORITHMS; COMPRESSIBILITY; INCOMPRESSIBLE FLOW; UNSTEADY FLOW; VISCOUS FLOW;

EID: 33745466381     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1700     Document Type: Article

References (33)

1. Chorin AJ. A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics 1997; 135:118-125
2. Comini G, Del Giudice S. Finite element solution of incompressible Navier-Stokes equations. Numerical Heat Transfer: Part A 1972; 5:463-478.
3. Schneider GE, Raithby GD, Yovanovich MM. Finite analysis of incompressible fluid flow incorporating equal order pressure and velociy interpolation. Numerical Methods in Luminar and Turbunent Flow. Pentech: Plymouth, 1978.
4. Oden JT, Wellford LC, Analysis of flow of viscous fluids by finite element method. AIAA Journal 1972; 10:1590-1599.
5. Zienkiewicz OC, Taylor RL, Nithiarasu P. The Finite Element Method for Fluid Dynamics. Butterworth and Heinemann: Stoneham, MA, 2005.
6. Taylor C, Hood P. A numerical solution of the Navier-Stokes equations using the finite element technique. Computer and Fluids 1973; 1:73-100.
7. Chung TJ. Computational Fluid Dynamics. Cambridge University Press: Cambridge, 2002.
8. Gresho PM, Sani RL. Incompressible Flow and the Finite Element Method. Wiley: New York, 1998.
9. Lewis RW, Nithiarasu P, Seetharamu KN. Fundamentals of the Finite Element Method for Heat and Fluid Flow. Wiley: New York, 2004.
10. Spalding DB. A novel finite difference formulation for differential equations involving both first and second order derivatives. International Journal for Numerical Methods in Engineering 1972; 4:551-559.
11. Brooks AN, Hughes TRJ. A streamline upwind/Petrov-Galerkin finite element formulation for advection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
12. de Sampaio PAB, Lyra PRM, Morgan K, Weatherill NP. Petrov-Galerkin solutions of the incompressible Navier-Stokes equations in primitive variables with adaptive remeshing. Computer Methods in Applied Mechanics and Engineering 1993; 106:143-178.
13. Zienkiewicz OC, Codina R. A general algorithm for compressible and incompressible flow. Part I. The split characteristic based scheme. International Journal for Numerical Methods in Fluids 1995; 20:869-885.
14. Massarotti N, Nithiarasu P, Zienkiewicz OC. Characteristic-Based-Split (CBS) algorithm for incompressible flow problems with heat transfer. International Journal for Numerical Methods in Heat and Fluid Flow 1998; 8:969-990.
15. Langtangen HP, Mardal KA, Winther R. Numerical methods for incompressible viscous flow. Advances in Water Resources 2002; 25:1125-1146.
16. Nithiarasu P. An efficient artificial compressibility (AC) scheme based on split (CBS) method for incompressible flows. International Journal for Numerical Methods in Engineering 2003; 56:1815-1845.
17. Malan AG, Lewis RW, Nithiarasu P. An improved unsteady, unsctructured, artificial compressibility, finite volume scheme for viscous incompressible flows: part I. Theory and implementation. International Journal for Numerical Methods in Engineering 2002; 54:695-714.
18. Nithiarasu P, Mathur JS, Weatherill NP, Morgan K, Three dimensional incompressible flow calculations using the Characteristic Based Split (CBS) scheme. International Journal for Numerical Methods in Fluids 2004; 44:1207-1229.
19. Hannani SK, Stanislas M, Dupont P. Incompressible Navier-Stokes computations with SUPG and GLS formulations. A comparison study. Computer Methods in Applied Mechanics and Engineering 1993; 106: 143-178.
20. Tamamidis P, Zhang G, Assanis DN. Comparison of pressure-based and artificial compressibility methods for solving 3D steady incompressible viscous flows. Journal of Computational Physics 1996; 124(1):1-13.
21. Codina R, Zienkiewicz OC. CBS versus GLS stabilization of the incompressible Navier-Stokes equations and the role of time step as stabilization parameter. Communications in Numerical Methods in Engineering 2002; 18:99-112.
22. Yuan L. Comparison of implicit multigrid schemes for three-dimensional incompressible flows. Journal of Computational Physics 2002; 117(1):134-155.
23. Brezzi F, Fortin M. Mixed and Hybrid Finite Element Methods. Springer: Berlin, 1991.
24. Codina R. Numerical solution of the incompressible Navier-Stokes Equations with Coriolis forces based on the discretization of the total time derivative. Journal of Computational Physics 1999; 148:467-496.
25. Ghia U, Ghia KN, Shin CT. High-resolutions for incompressible flow using the Navier-Stokes equations and multigrid method. Journal of Computational Physics 1982; 48:387-411.
26. Denham MK, Patrik MA. Laminar flow over a downstream-facing in a two-dimensional flow channel. Transactions of the Institution of Chemical Engineers 1974; 52:361-367.
27. Ichinose K, Tokunaga H, Satofuka N. Numerical simulation of two-dimesnional backward-facing step flows. Transactions of JSME B 1991; 57(543):3715-3721.
28. Aung W. An experimental study of laminar heat transfer downstream of backsteps. Journal of Heat Transfer 1983; 105:823-829.
29. Malan AG, Lewis RW, Nithiarasu P. An improved unsteady, unsctructured, artificial compressibility, finite volume scheme for viscous incompressible flows: part II. Application. International Journal for Numerical Methods in Engineering 2002; 54:715-729.
30. de Vahl Davis G. Natural convection of air in a square cavity: a benchmark numerical solution. International Journal for Numerical Methods in Fluids 1983; 3:249-264.
31. Le Quere P, Alziary de Roquefort T. Computation on natural convection in two-dimensional cavities with Chebyshev polynomial. Journal of Computational Physics 1985; 57:210-228.
32. Barakos G, Mitsoulis E, Assimacopoulos D. Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions. International Journal for Numerical Methods in Fluids 1994; 18:695-719.
33. Wan DC, Patnaik BSV, Wei GW. A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution. Numerical Heat Transfer: Part B 2001; 40:199-228.