Steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility (AC)-based characteristic-based split (CBS) scheme
In this paper, the explicit characteristic‐based split (CBS) scheme has been employed to solve both steady and unsteady flows inside a non‐rectangular double driven cavity. This problem is recently suggested as a benchmark problem for incompressible flows. Both unstructured and structured meshes hav...
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| Published in | International journal for numerical methods in engineering Vol. 63; no. 3; pp. 380 - 397 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
21.05.2005
Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0029-5981 1097-0207 |
| DOI | 10.1002/nme.1280 |
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| Abstract | In this paper, the explicit characteristic‐based split (CBS) scheme has been employed to solve both steady and unsteady flows inside a non‐rectangular double driven cavity. This problem is recently suggested as a benchmark problem for incompressible flows. Both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible. The results obtained show the existence of steady state at lower Reynolds numbers (⩽1000) and transient states at higher Reynolds numbers. The flow approaches a turbulent state as the Reynolds number is increased to 10 000. Copyright © 2005 John Wiley & Sons, Ltd. |
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| AbstractList | In this paper, the explicit characteristic‐based split (CBS) scheme has been employed to solve both steady and unsteady flows inside a non‐rectangular double driven cavity. This problem is recently suggested as a benchmark problem for incompressible flows. Both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible. The results obtained show the existence of steady state at lower Reynolds numbers (⩽1000) and transient states at higher Reynolds numbers. The flow approaches a turbulent state as the Reynolds number is increased to 10 000. Copyright © 2005 John Wiley & Sons, Ltd. In this paper, the explicit characteristic-based split (CBS) scheme has been employed to solve both steady and unsteady flows inside a non-rectangular double driven cavity. This problem is recently suggested as a benchmark problem for incompressible flows. Both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible. The results obtained show the existence of steady state at lower Reynolds numbers (1000) and transient states at higher Reynolds numbers. The flow approaches a turbulent state as the Reynolds number is increased to 10 000. |
| Author | Nithiarasu, P. Liu, C.-B. |
| Author_xml | – sequence: 1 givenname: P. surname: Nithiarasu fullname: Nithiarasu, P. email: P.Nithiarasu@swansea.ac.uk organization: Civil and Computational Engineering Centre, School of Engineering, University of Wales Swansea, Swansea SA2 8PP, U.K – sequence: 2 givenname: C.-B. surname: Liu fullname: Liu, C.-B. organization: Civil and Computational Engineering Centre, School of Engineering, University of Wales Swansea, Swansea SA2 8PP, U.K |
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| Cites_doi | 10.1016/0021-9991(90)90204-E 10.1002/(SICI)1097-0363(19990915)31:1<359::AID-FLD984>3.0.CO;2-7 10.1016/0021-9991(82)90058-4 10.1002/fld.1650050606 10.1002/(SICI)1097-0207(19980330)41:6<1153::AID-NME334>3.0.CO;2-9 10.1017/S0022112066000545 10.1016/0021-9991(82)90032-8 10.1115/1.3243136 10.1016/S0997-7546(98)80011-3 10.1002/nme.447 10.1016/0021-9991(83)90129-8 10.1017/S0022112096004727 10.1016/0021-9991(79)90160-8 10.1002/nme.712 10.1006/jcph.1996.0041 10.1108/09615539910297932 10.1002/fld.1650200812 10.1002/nme.674 10.1016/0021-9991(73)90157-5 10.1016/0021-9991(67)90037-X 10.1108/09615539810201839 10.1002/nme.1620340218 10.1002/nme.443 10.1016/0021-9991(87)90182-3 10.1017/S002211206700237X 10.1007/s001620050138 10.1016/0045-7930(88)90023-0 10.1016/0021-9991(86)90035-5 |
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| Keywords | Method of characteristics matrix free method Transient response Compressibility Turbulent flow Reynolds number Steady flow Step method Data structures Unsteady flow Cavity flow Steady state dual time stepping Cavities Incompressible flow double driven cavity CBS scheme Matrix method Incompressible fluid Mesh generation |
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| References | Goodrich JW, Gustafson K, Halasi K. Hopf bifurcation in the driven cavity. Journal of Computational Physics 1990; 90:219-261. 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 2003, to appear. 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. Schreiber R, Keller HB. Driven cavity flows by efficient numerical techniques. Journal of Computational Physics 1983; 49:310-333. Kuhlmann HC, Wanschura M, Rath HJ. Elliptic instability in two-sided lid-driven cavity flow. European Journal of Mechanics - B/Fluids 1998; 17:561-569. Nithiarasu P. An efficient artificial compressibility (AC) scheme based on the characteristic based split (CBS) method for incompressible flows. International Journal for Numerical Methods in Engineering 2003; 56:1815-1845. Nithiarasu P, Seetharamu KN, Sundararajan T. Finite element analysis of transient natural convection in an odd-shapped enclosure. International Journal of Numerical Methods for Heat and Fluid Flow 1998; 8:199-216. 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. Albensoeder S, Kuhlmann HC, Rath HJ. Multiplicity of steady two-dimensional flows in two-sided lid-driven cavities. Theoretical and Computational Fluid Dynamics 2001; 14:223-241. Chorin AJ. A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics 1967; 2:12-26. Kuhlmann HC, Wanschura M, Rath HJ. Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures. Journal of Fluid Mechanics 1997; 336:267-299. Manzari MT. An explicit finite element algorithm for convection heat transfer problems. International Journal of Numerical Methods for Heat and Fluid Flow 1999; 9:860-877. Gustafson K, Halasi K. Vortex dynamics of cavity flows. Journal of Computational Physics 1986; 64:279-319. 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; 124:1-13. Gustafson K, Halasi K. Cavity flow dynamics at higher Reynolds number and higher aspect ratio. Journal of Computational Physics 1987; 70:271-283. Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48:387-411. Burggraf OR. Analytical and numerical studies of the structure of steady separated flows. Journal of Fluid Mechanics 1966; 24:113-151. Zienkiewicz OC, Nithiarasu P, Codina R, Vázquez M, Ortiz P. An efficient and accurate algorithm for fluid mechanics problems. The characteristic based split (CBS) algorithm. International Journal for Numerical Methods in Fluids 1999; 31:359-396. Ramaswamy B. Finite element solution for advection and natural convection flows. Computers and Fluids 1988; 16:349-388. 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. Gaitonde AL. A dual time method for two dimensional incompressible flow calculations. International Journal for Numerical Methods in Engineering 1998; 41:1153-1166. Benjamin AS, Denny VE. On the convergence of numerical solutions for 2-D flows in a cavity at large Re. Journal of Computational Physics 1979; 33:340-358. 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. Freitas CJ, Street RL, Findikakis AN, Koseff JR. Numerical simulation of three-dimensional flow in a cavity. International Journal for Numerical Methods in Fluids 1985; 5:561-575. Zhou YC, Patnaik BSV, Wan DC, Wei GW. DSC solution for flow in a staggered double lid driven cavity. International Journal for Numerical Methods in Engineering 2003; 57:211-234. Comini G, Del Guidice S. Finite element solution of incompressible Navier-Stokes equations. Numerical Heat Transfer: Part A 1972; 5:463-478. Gatski TB, Grosch CE, Rose ME. A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables. Journal of Computational Physics 1982; 48:1-22. Pan F, Acrivos A. Steady flows in rectangular cavities. Journal of Fluid Mechanics 1967; 28:643-655. Bozeman JD, Dalton C. Numerical study of viscous flow in a cavity. Journal of Computational Physics 1973; 12:348-363. Gresho P, Sani RL. Incompressible Flow and the Finite Element Method. Wiley: Chichester, 1999. Koseff JR, Street RL. The lid-driven cavity: a synthesis of qualitative and quantitative observations. Journal of Fluids Engineering (ASME) 1984; 106:390-398. 1997; 336 1985; 5 1973; 12 1987; 70 2000; 3 1984; 106 2002; 54 1988; 16 1967; 28 2003; 57 2003 1998; 41 1972; 5 1979; 33 1996; 124 1992; 34 2003; 56 1999; 9 1999 1995; 20 1982; 48 1998; 17 1986; 64 1967; 2 1999; 31 1966; 24 1983; 49 1990; 90 2001; 14 1998; 8 Ghia (10.1002/nme.1280-BIB5) 1982; 48 Nithiarasu (10.1002/nme.1280-BIB17) 2003; 56 Kuhlmann (10.1002/nme.1280-BIB13) 1997; 336 Gresho (10.1002/nme.1280-BIB28) 1999 Nithiarasu (10.1002/nme.1280-BIB31) 1998; 8 Albensoeder (10.1002/nme.1280-BIB14) 2001; 14 Gaitonde (10.1002/nme.1280-BIB21) 1998; 41 Kuhlmann (10.1002/nme.1280-BIB15) 1998; 17 Zhou (10.1002/nme.1280-BIB16) 2003; 57 Ramaswamy (10.1002/nme.1280-BIB30) 1988; 16 Gustafson (10.1002/nme.1280-BIB11) 1987; 70 Malan (10.1002/nme.1280-BIB18) 2002; 54 Zienkiewicz (10.1002/nme.1280-BIB26) 2000; 3 Freitas (10.1002/nme.1280-BIB9) 1985; 5 Bozeman (10.1002/nme.1280-BIB3) 1973; 12 Benjamin (10.1002/nme.1280-BIB4) 1979; 33 Gustafson (10.1002/nme.1280-BIB10) 1986; 64 Ramaswamy (10.1002/nme.1280-BIB32) 1992; 34 Zienkiewicz (10.1002/nme.1280-BIB25) 1999; 31 Schreiber (10.1002/nme.1280-BIB7) 1983; 49 Gatski (10.1002/nme.1280-BIB6) 1982; 48 Chorin (10.1002/nme.1280-BIB27) 1967; 2 Nithiarasu (10.1002/nme.1280-BIB23) 2003 Tamamidis (10.1002/nme.1280-BIB20) 1996; 124 Zienkiewicz (10.1002/nme.1280-BIB24) 1995; 20 Koseff (10.1002/nme.1280-BIB8) 1984; 106 Comini (10.1002/nme.1280-BIB29) 1972; 5 Burggraf (10.1002/nme.1280-BIB1) 1966; 24 Goodrich (10.1002/nme.1280-BIB12) 1990; 90 Pan (10.1002/nme.1280-BIB2) 1967; 28 Malan (10.1002/nme.1280-BIB19) 2002; 54 Manzari (10.1002/nme.1280-BIB22) 1999; 9 |
| References_xml | – reference: Nithiarasu P, Seetharamu KN, Sundararajan T. Finite element analysis of transient natural convection in an odd-shapped enclosure. International Journal of Numerical Methods for Heat and Fluid Flow 1998; 8:199-216. – reference: 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. – reference: Goodrich JW, Gustafson K, Halasi K. Hopf bifurcation in the driven cavity. Journal of Computational Physics 1990; 90:219-261. – reference: Gresho P, Sani RL. Incompressible Flow and the Finite Element Method. Wiley: Chichester, 1999. – reference: Burggraf OR. Analytical and numerical studies of the structure of steady separated flows. Journal of Fluid Mechanics 1966; 24:113-151. – reference: Freitas CJ, Street RL, Findikakis AN, Koseff JR. Numerical simulation of three-dimensional flow in a cavity. International Journal for Numerical Methods in Fluids 1985; 5:561-575. – reference: Bozeman JD, Dalton C. Numerical study of viscous flow in a cavity. Journal of Computational Physics 1973; 12:348-363. – reference: Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48:387-411. – reference: Comini G, Del Guidice S. Finite element solution of incompressible Navier-Stokes equations. Numerical Heat Transfer: Part A 1972; 5:463-478. – reference: Benjamin AS, Denny VE. On the convergence of numerical solutions for 2-D flows in a cavity at large Re. Journal of Computational Physics 1979; 33:340-358. – reference: Manzari MT. An explicit finite element algorithm for convection heat transfer problems. International Journal of Numerical Methods for Heat and Fluid Flow 1999; 9:860-877. – reference: Zienkiewicz OC, Nithiarasu P, Codina R, Vázquez M, Ortiz P. An efficient and accurate algorithm for fluid mechanics problems. The characteristic based split (CBS) algorithm. International Journal for Numerical Methods in Fluids 1999; 31:359-396. – reference: 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 2003, to appear. – reference: Chorin AJ. A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics 1967; 2:12-26. – reference: Gustafson K, Halasi K. Cavity flow dynamics at higher Reynolds number and higher aspect ratio. Journal of Computational Physics 1987; 70:271-283. – reference: Gaitonde AL. A dual time method for two dimensional incompressible flow calculations. International Journal for Numerical Methods in Engineering 1998; 41:1153-1166. – reference: 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; 124:1-13. – reference: 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. – reference: Gatski TB, Grosch CE, Rose ME. A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables. Journal of Computational Physics 1982; 48:1-22. – reference: Zhou YC, Patnaik BSV, Wan DC, Wei GW. DSC solution for flow in a staggered double lid driven cavity. International Journal for Numerical Methods in Engineering 2003; 57:211-234. – reference: Schreiber R, Keller HB. Driven cavity flows by efficient numerical techniques. Journal of Computational Physics 1983; 49:310-333. – reference: Albensoeder S, Kuhlmann HC, Rath HJ. Multiplicity of steady two-dimensional flows in two-sided lid-driven cavities. Theoretical and Computational Fluid Dynamics 2001; 14:223-241. – reference: 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. – reference: Gustafson K, Halasi K. Vortex dynamics of cavity flows. Journal of Computational Physics 1986; 64:279-319. – reference: Kuhlmann HC, Wanschura M, Rath HJ. Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures. Journal of Fluid Mechanics 1997; 336:267-299. – reference: Koseff JR, Street RL. The lid-driven cavity: a synthesis of qualitative and quantitative observations. Journal of Fluids Engineering (ASME) 1984; 106:390-398. – reference: Kuhlmann HC, Wanschura M, Rath HJ. Elliptic instability in two-sided lid-driven cavity flow. European Journal of Mechanics - B/Fluids 1998; 17:561-569. – reference: Pan F, Acrivos A. Steady flows in rectangular cavities. Journal of Fluid Mechanics 1967; 28:643-655. – reference: 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. – reference: Ramaswamy B. Finite element solution for advection and natural convection flows. Computers and Fluids 1988; 16:349-388. – reference: Nithiarasu P. An efficient artificial compressibility (AC) scheme based on the characteristic based split (CBS) method for incompressible flows. 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| SubjectTerms | CBS scheme Computational techniques double driven cavity dual time stepping Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) General theory incompressible flow Mathematical methods in physics matrix free method Physics |
| Title | Steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility (AC)-based characteristic-based split (CBS) scheme |
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