A Eulerian-Lagrangian method applied to fluid flow in lid-driven cavities with irregular bottom walls

Numerical Heat Transfer, Part B: Fundamentals

Volumn 53, Issue 3, 2008, Pages 206-233

  Mariani, Viviana Cocco ^a   Prata, Alvaro Toubes ^b  

^a PONTIFICAL CATHOLIC UNIVERSITY OF PARANÁ   (Brazil)

^b FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

BENCHMARKING; FINITE VOLUME METHOD; MOMENTUM; REYNOLDS NUMBER; VELOCITY MEASUREMENT;

EULERIAN LAGRANGE METHOD; IRREGULAR BOTTOM WALLS;

FLOW OF FLUIDS;

EID: 38349124229     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/10407790701632568     Document Type: Article

References (36)

1. J. R. Koseff and R. L. Street, The Lid-Driven Cavity Flow: A Synthesis of Qualitative and Quantitative Observations, ASME J. Fluids Eng., vol. 106, pp. 390-398, 1984.
2. U. Ghia, K. N. Ghia, and C. T. Shin, High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multi-Grid Method, J. Comput. Phys., vol. 48, pp. 387-411, 1982.
3. C. J. Freitas, R. L. Street, A. N. Findikakis, and J. R. Koseff, Numerical Simulation of Three-Dimensional Flow in a Cavity, Int. J. Numer. Meth. Fluids, vol. 5, pp. 561-575, 2005.
4. S. P. Vanka, Block-Implicit Multigrid Solution of Navier-Stokes Equations in Primitive Variables, J. Comput. Phys., vol. 65, pp. 138-158, 1986.
5. A. T. Prata and E. M. Sparrow, Evaporative Mass and Heat Transfer From a Lid-Driven Cavity, Numer. Heat Transfer, vol. 13, pp. 27-48, 1988.
6. C.-H. Bruneau and C. Jouron, An Efficient Scheme for Solving Steady Incompressible Navier-Stokes Equations, J. Comput. Phys., vol. 89, pp. 389-413, 1990.
7. S. Hou, Q. Zou, S. Chen, G. Doolen, and A. Cogley, Simulation of Cavity Flows by the Lattice Boltzmann Method, J. Comput. Phys., vol. 118, pp. 329-347, 1995.
8. E. Barragy and G. F. Carey, Stream Function-Vorticity Driven Cavity Solution Using p Finite Elements, Comput. Fluids, vol. 26, pp. 453-468, 1997.
9. O. Botella and R. Peyret, Benchmark Spectral Results on the Lid-Driven Cavity Flow, Comput. Fluids, vol. 27, pp. 421-433, 1998.
10. M. M. Gupta and J. C. Kalita, A New Paradigm for Solving Navier-Stokes Equations: Stream Function-Velocity Formulation, J. Comput. Phys., vol. 207, pp. 52-68, 2005.
11. C.-H. Bruneau and M. Saad, The 2D Lid-Driven Cavity Problem Revisited, Comput. Fluids, vol. 35, pp. 326-348, 2006.
12. W. D. McQuain, C. J. Ribbens, C.-Y. Wang, and L. T. Watson, Steady Viscous Flow in a Trapezoidal Cavity, Comput. Fluids, vol. 23, pp. 613-626, 1994.
13. J. J. Quirk, An Alternative to Unstructured Grids for Computing Gas Dynamic Flows around Arbitrarily Complex Two Dimensional Bodies, ICASE Rep. 92-7, NASA Langley Research Center, Hampton, VA, 1992.
14. R. Jyotsna and P. Vanka, Multigrid Calculation of Steady, Viscous Flow in a Triangular Cavity, J. Comput. Phys., vol. 122, pp. 107-117, 1995.
15. M.-H. Chang and C.-H. Cheng, Predictions of Lid-Driven Flow and Heat Convection in an Arc-Shape Cavity, Int. Commun. Heat Mass Transfer, vol. 26, pp. 829-838, 1999.
16. C. Migeon, A. Texier, and G. Pineau, Effects of Lid-Driven Cavity Shape on the Flow Establishment Phase, J. Fluids Struct., vol. 14, pp. 469-488, 2000.
17. C. J. Ribbens, L. T. Watson, and C.-Y. Wang, Steady Viscous Flow in a Triangular Cavity, J. Comput. Phys., vol. 112, pp. 173-181, 1994.
18. M. Li and T. Tang, Steady Viscous Flow in a Triangular Cavity by Efficient Numerical Techniques, Comput. Math. Appl., vol. 31, pp. 55-65, 1995.
19. F. E. Ham, F. S. Lien, and A. B. Strong, A Cartesian Grid Method with Transient Anisotropic Adaptation, J. Comput. Phys., vol. 179, pp. 469-494, 2002.
20. C.-H. Cheng and C.-L. Chen, Buoyancy-Induced Periodic Flow and Heat Transfer in Lid-Driven Cavities with Different Cross-Sectional Shapes, Int. Commun. Heat Mass Transfer, vol. 32, pp. 483-490, 2005.
21. H. Xu, C. Zhang, and R. Barron, Numerical Simulation of Cavity Flows Based on Transformed Equations, Appl. Math. Comput., vol. 176, pp. 506-515, 2006.
22. C. S. Peskin, Numerical-Analysis of Blood-Flow in Heart, J. Comput. Phys., vol. 25, pp. 220-252, 1977.
23. H. S. Udaykumar and W. Shyy, Simulation of Interfacial Instabilities During Solidification; Part I: Conduction and Capillarity Effects, Numer. Heat Transfer B, vol. 27, pp. 127-155, 1994.
24. S. A. Bayyuk, K. G. Powell, and B. can Leer, A Simulation Technique for 2-D Unsteady Inviscid Flows around Arbitrarily Moving and Deforming Bodies of Arbitrary Geometry, AIAA paper 93-3391, 1993.
25. H. S. Udaykumar, W. Shyy, and M. M. Rao, ELAFINT: A Mixed Eulerian-Lagrangian Method for Fluid Flows with Complex and Moving Boundaries, Int. J. Numer. Meth. Fluids, vol. 22, pp. 691-712, 1996.
26. T. Ye, R. Mittal, H. S. Udaykumar, and W. Shyy, A Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries, 37th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 1999.
27. S. V. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.
28. H. S. Udaykumar, H.-C. Kan, W. Shyy, and R. Tay-Son-Tran, Multiphase Dynamics in Arbitrary Geometries on Fixed Cartesian Grids, J. Comput. Phys., vol. 137, pp. 366-405, 1997.
29. W. Shyy, H. S. Udaykumar, M. M. Rao, and R. W. Smith, Computational Fluid Dynamics with Moving Boundaries, Taylor & Francis, Bristol, PA, 1996.
30. Z. G. Qu, W. Q. Tao, and Y. L. He, An Improved Numerical Scheme for the SIMPLER Method on Nonorthogonal Curvilinear Coordinates: SIMPLERM, Numer. Heat Transfer B, vol. 51, pp. 43-66, 2007.
31. B. Yu, H. Ozoe, and W. Q. Tao, A Modified Pressure-Correction Scheme for the SIMPLER Method, MSIMPLER, Numer. Heat Transfer B, vol. 39, pp. 435-449, 2001.
32. M. M. Rahman and T. Siikonen, An Improved Simple Method on a Collocated Grid, Numer. Heat Transfer B, vol. 38, pp. 177-201, 2000.
33. Y. Sheng, M. Shoukri, G. Sheng, and P. Wood, A Modification to the SIMPLE Method for Buoyancy-Driven Flows, Numer. Heat Transfer B, vol. 33, pp. 65-78, 1998.
34. T. Hayase, J. C Humphrey, and R. Greif, A Consistently Formulated QUICK Scheme for Fast and Stable Convergence Using Finite-Volume Iterative Calculation Procedures, J. Comput. Phys., vol. 98, pp. 108-118, 1992.
35. P. J. Roache, A Method for Uniform Reporting of Grid Refinement Studies, in Quantification of Uncertainty in Computational Fluid Dynamics, ASME FED-Vol. 158, pp. 109-120, 1993.
36. R. Glowinski, G. Guidoboni, and T.-W. Pan, Wall-Driven Incompressible Viscous Flow in a Two-Dimensional Semi-Circular Cavity, J. Comput. Phys., vol. 216, pp. 76-91, 2006.