Three-dimensional incompressible flow calculations using the characteristic based split (CBS) scheme

International Journal for Numerical Methods in Fluids

Volumn 44, Issue 11, 2004, Pages 1207-1229

  Nithiarasu, P ^a   Mathur, J S ^a   Weatherill, N P ^a   Morgan, K ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Artificial compressibility; CBS scheme; Explicit; Incompressible flow; Porous media flow; Semi implicit; Velocity correction

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; INCOMPRESSIBLE FLOW; ISOTHERMS; MATHEMATICAL MODELS;

INCOMPRESSIBLE VISCOUS FLOW; ISOTHERMAL IMCOMPRESSIBLE FLOWS;

VISCOUS FLOW;

INCOMPRESSIBLE FLOW; MATHEMATICAL ANALYSIS; MODELING; THREE-DIMENSIONAL FLOW;

EID: 1842735161     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.682     Document Type: Article

References (50)

1. Morgan K, Peraire J. Unstructured grid finite element methods for fluid mechanics. Reports on Progress in Physics 1998; 61:569-638.
2. Sorensen KA, Hassan O, Morgan K, Weatherill NP. Agglomerated multigrid on hybrid unstructured meshes for compressible flow. International Journal for Numerical Methods in Fluids 2002; 40:593-603.
3. Tezduyar TE, Finite element methods for flow problems with moving boundaries and interfaces. Archives of Computational Mechanics in Engineering 2001; 8:83-130.
4. Lanteri S. Parallel solutions of compressible flows using overlapping and non-overlapping mesh partitioning strategies. Parallel Computing 1996; 22:943-968.
5. Weatherill NP, Hassan O, Morgan K, Jones JW, Larwood B. Towards fully parallel aerospace simulations on unstructured meshes. Engineering Computations 2001; 18:347-375.
6. Morgan K, Weatherill NP, Hassan O, Brookes PJ, Said R, Jones J. A parallel framework for multidisciplinary aerospace engineering simulations using unstructured meshes. International Journal for Numerical Methods in Fluids 1999; 31:159-173.
7. Moinier P, Giles MB. Stability analysis of preconditioned approximations of the Euler equations on unstructured meshes. Journal of Computational Physics 2002; 178:498-519.
8. Löhner R. Applied CFD Techniques. Wiley: New York, 2001.
9. Zienkiewicz OC, Taylor RL. The finite element method. Fluid Dynamics (5th edn), vol. 3. Butterworth-Heinemann: London, 2000.
10. Weatherill NP, Turner-Smith EA, Jones J, Morgan K, Hassan O. An integrated software environment for multidisciplinary computational engineering. Engineering Computations 1999; 16:913-933.
11. Chorin AJ. Numerical solution of the Navier-Stokes equations. Mathematics of Computation 1968; 23:341-354.
12. Comini G, Del Guidice S. Finite element solution of incompressible Navier-Stokes equations. Numerical Heat Transfer, Part A 1972; 5:463-478.
13. Ramaswamy B. Finite element solution for advection and natural convection flows. Computers and Fluids 1988; 16:349-388.
14. Ramaswamy B, Jue TC, Akin JE. Semi-implicit and explicit finite element schemes for coupled fluid thermal problems. International Journal for Numerical Methods in Engineering 1992; 34:675-696.
15. Gresho PM, Sani RL. Incompressible Flow and the Finite Element Method. Wiley: New York, 2000.
16. 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.
17. Zienkiewicz OC, Satya Sai BVK, Morgan K, Codina R, Vázquez M. A general algorithm for compressible and incompressible flow-Part II: tests on the explicit form. International Journal for Numerical Methods in Fluids 1995; 20:887-913.
18. Codina R, Vázquez M, Zienkiewicz OC. A general algorithm for compressible and incompressible flows. Part III: The semi-implicit form. International Journal for Numerical Methods in Fluids 1998; 27:13-32.
19. Zienkiewicz OC, Sai BVKS, Morgan K, Codina R. Split, characteristic based semi-implicit algorithm for laminar/turbulent incompressible flows. International Journal for Numerical Methods in Fluids 1996; 23: 787-809.
20. Zienkiewicz OC, Nithiarasu P, Codina R, Vázquez M, Ortiz P. The characteristic-based-split procedure: An efficient and accurate algorithm for fluid problems. International Journal for Numerical Methods in Fluids 1999; 31:359-392.
21. Zienkiewicz OC, Nithiarasu P. A universal algorithm for fluid dynamics. The characteristic based split (CBS) procedure. Some tests on stability and boundary conditions. Archives of Mechanics 2000; 52:857-887.
22. Nithiarasu P, Zienkiewicz OC. On stabilization of the CBS algorithm. Internal and external time steps. International Journal for Numerical Methods in Engineering 2000; 48:875-880.
23. Nithiarasu P. On boundary conditions of the characteristic based split (CBS) algorithm for fluid dynamics. International Journal for Numerical Methods in Engineering 2002; 54:523-536.
24. Massarotti N, Nithiarasu P, Zienkiewicz OC. Characteristic-based-split (CBS) algorithm for incompressible flow problems with heat transfer. International Journal of Numerical Methods for Heat and Fluid Flow 1998; 8: 969-990.
25. Nithiarasu P. An efficient artificial compressibility (AC) method based on the characteristic based split (CBS) method for incompressible flows. International Journal for Numerical Methods in Engineering 2003; 56: 1815-1845.
26. Turkel E. Review of preconditioning methods for fluid dynamics. Applied Numerical Mathematics 1993; 12: 257-284.
27. Weiss JW, Smith WA. Preconditioning applied to variable and constant density flows. AIAA Journal 1995; 33:2050-2057.
28. Choi YH, Merkle CL. The application of preconditioning in viscous flows. Journal of Computational Physics 1993; 105:207-223.
29. Turkel E. Preconditioning methods for solving the incompressible and low speed compressible equations. Journal of Computational Physics 1987; 72:227-298.
30. Gaitonde AL. A dual time method for two dimensional incompressible flow calculations. International Journal for Numerical Methods in Engineering 1998; 41:1153-1166.
31. Malan AG, Lewis RW, Nithiarasu P. An improved unsteady, unstructured, 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.
32. Whitaker S. Diffusion and dispersion in porous media. AIChE Journal 1961; 13:420-427.
33. Vafai K, Tien CL. Boundary and inertia effects on flow and heat transfer in porous media. International Journal of Heat and Mass Transfer 1981; 24:195-203.
34. Hsu CT, Cheng P. Thermal dispersion in a porous medium. International Journal of Heat and Mass Transfer 1990; 33:1587-1597.
35. Nithiarasu P, Seetharamu KN, Sundararajan T. Double-diffusive natural convection in an enclosure filled with fluid saturated porous medium-a generalised non-Darcy approach. Numerical Heat Transfer, Part A 1996; 30:413-426.
36. Nithiarasu P, Seetharamu KN, Sundararajan T. Natural convective heat transfer in a fluid saturated variable porosity medium. International Journal of Heat and Mass Transfer 1997; 40:3955-3967.
37. Nithiarasu P, Ravindran K. A new semi-implicit time stepping procedure for buoyancy driven flow in a fluid saturated porous medium. Computer Methods in Applied Mechanics and Engineering 1998; 165:147-154.
38. Nithiarasu P, Seetharamu KN, Sundararajan T. Finite element modelling of flow, heat and mass transfer in fluid saturated porous media. Archives of Computational Methods in Engineering, State of the art reviews 2002; 9:3-42.
39. Nithiarasu P. A comparative study on the performance of two time stepping schemes for convection in a fluid saturated porous medium. International Journal for Numerical Methods in Heat and Fluid Flow 2001; 11: 308-328.
40. Massarotti N, Nithiarasu P, Zienkiewicz OC. Natural convection in porous medium-fluid interface problems-a finite element analysis by using the CBS procedure. International Journal for Numerical Methods in Heat and Fluid flow 2001; 11:473-490.
41. Nithiarasu P, Seetharamu KN, Sundararajan T. Finite element analysis of transient natural convection in an odd-shapped enclosure. International Journal for Numerical Methods in Heat and Fluid Flow 1998; 8: 199-216.
42. Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and multigrid method. Journal of Computational Physics 1982; 48:387-411.
43. Denham MK, Patrik MA. Laminar flow over a downstream-facing step in a two-dimensional flow channel. Transactions of the Institution of Chemical Engineers 1974; 52:361-367.
44. Gulçat Ü, Aslan AR. Accurate 3D viscous incompressible flow calculations with FEM. International Journal for Numerical Methods in Fluids 1997; 25:985-1001.
45. Rimon Y, Cheng SI. Numerical solution of a uniform flow over a sphere at intermediate Reynolds numbers. The Physics of Fluids 1969; 12:949-959.
46. Davis G de V. Natural convection of air in a square cavity: a bench mark numerical solution. International Journal for Numerical Methods in Fluids 1983; 3:249-264.
47. de Sampaio PAB, Lyra PRM, Morgan K, Weatherill NP. Petrov-Galerkin solutions of the incompressible Navier-Stokes equations in primitive variables in with adaptive remeshing. Computer Methods in Applied Mechanics and Engineering 1993; 106:143-178.
48. Lee S. A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate Reynolds numbers. Computers and Fluids 2000; 29:639-667.
49. Malan AG, Lewis RW, Nithiarasu P. An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: part II. Application. International Journal for Numerical Methods in Engineering 2002; 54:715-729.
50. Kim J, Moin P. Application of a fractional step method to incompressible Navier-Stokes equations. Journal of Computational Physics 1985; 59:308-323.