A novel mlpg-finite-Volume mixed method for analyzing stokesian flows & study of a new vortex mixing flow

CMES - Computer Modeling in Engineering and Sciences

Volumn 71, Issue 4, 2011, Pages 363-395

  Avila, Ruben ^a   Han, Zhidong ^b   Atluri, Satya N ^b  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Chaotic advection; Meshless Local Petrov Galerkin approach (MLPG); Stokesian flows

Indexed keywords

ANALYTICAL SOLUTIONS; ANGULAR SPEED; CHAOTIC ADVECTION; COAXIAL CYLINDERS; ELLIPTICAL CROSS SECTION; FINITE-VOLUME; FLOW DOMAINS; FLOW GEOMETRIES; FLUID ELEMENT; MESHLESS INTERPOLATION; MESHLESS LOCAL PETROV-GALERKIN APPROACHES; MIXED METHOD; MLPG METHOD; NUMERICAL SIMULATION; PASSIVE FLUID; PRESSURE FIELD; SPATIAL DERIVATIVES; STEADY STATE; STOKES EQUATIONS; STOKES FLOWS; STOKESIAN FLOWS; STRAIN TENSOR; VELOCITY FIELD; VELOCITY VECTORS; VORTEX MIXING;

ADVECTION; CYLINDERS (SHAPES); EQUATIONS OF STATE; FINITE VOLUME METHOD; GALERKIN METHODS; TENSORS;

VELOCITY;

EID: 79955694856     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. Anderson, P. D.; Ternet, D.; Peters, G.W. M.; Meijer, H. E. H. (2006): Experimental/numerical analysis of chaotic advection in a three-dimensional cavity flow. Intern Polymer Processing, vol. 21, pp. 412-420. (Pubitemid 44594712)
2. Aref, H. (1984): Stirring by chaotic advection. J. Fluid Mechanics, vol. 143, pp. 1-21.
3. Aref, H. (2002): The development of chaotic advection. Physics of Fluids, vol. 14, pp. 1315-1325. (Pubitemid 34439815)
4. Aref, H.; Balachandar, S. (1986): Chaotic advection in a Stokes flow. Physics of Fluids, vol. 29, pp. 3515-3521.
5. Atluri, S. N. (2004): The Meshless Methods (MLPG) For Domain & Bie Discretizations. Tech Science Press.
6. Atluri, S. N.; Han, Z. D.; Rajendran, A. M. (2004): A new implementation of the meshless finite volume method, through the MLPG "Mixed approach". CMES: Computer Modeling in Engineering & Sciences, vol. 6, pp. 491-513. (Pubitemid 40020853)
7. Atluri, S. N.; Shen, S. (2002): The Meshless Local Petrov-Galerkin (MLPG) Method. Tech Science Press.
8. Atluri, S. N.; Shen, S. (2002): The Meshless Local Petrov-Galerkin (MLPG) method: A simple & less-costly alternative to the Finite Element and Boundary Element methods. CMES: Computer Modeling in Engineering & Sciences, vol. 3, pp. 11-51. (Pubitemid 135695145)
9. Atluri, S. N.; Zhu, T. (1998): A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, vol. 22, pp. 117-127. (Pubitemid 128620889)
10. Ballal, B. Y.; Rivlin, R. S. (1976): Flow of a Newtonian fluid between eccentric rotating cylinders: intertial effects. Arch. Rational Mech. Anal., vol. 62, pp. 237-294.
11. Bratianu, C.; Atluri, S. N. (1983): A Hybrid finite element method for Stokes flow: Part I-formulation and numerical studies. Computer Methods in Applied Mechanics and Engineering, vol. 36, pp. 23-37.
12. Brezzi, F.; Fortin, M. (1991): Mixed and Hybrid Finite Element Methods. Springer-Verlag.
13. Chaiken, J.; Chevray, R.; Tabor, M.; Tan, Q. M. (1986): Experimental study of Lagrangian turbulence in a Stokes flow. Proc. R. Soc. Lond. A, vol. 408, pp. 165-174. (Pubitemid 17494933)
14. Chaiken, J.; Chu, C. K.; Tabor, M.; Tan, Q. M. (1987): Lagrangian turbulence and spatial complexity in a Stokes flow. Physics of Fluids, vol. 30, pp. 687-694.
15. Hwang, W. R.; Anderson, P. D.; Hulsen, M. A. (2005): Chaotic advection in a cavity flow with rigid particles. Physics of Fluids, vol. 17, 043602.
16. Jana, S. C.; Metcalfe, G.; Otino, J. M. (1994): Experimental and computational studies of mixing in complex Stokes flows: the vortex mixing flow and multicellular cavity flows. J. Fluid Mechanics, vol. 269, pp. 199-246. (Pubitemid 283256)
17. Kang, T. G.; Hulsen, M. A.; Anderson, P. D.; den Toonder, J. M. J.; Meijer, H. E. H. (2007): Chaotic advection using passive and externally actuated particles in a serpentine channel flow. Chemical Engineering Science, vol. 62, pp. 6677-6686. (Pubitemid 47599470)
18. Karniadakis, G.; Beskok, A.; Aluru, N. (2005): Microflows and Nanoflows: Fundamentals and Simulation. Springer.
19. Lin, H.; Atluri, S. N. (2000): Meshless Local Petrov Galerkin (MLPG) method for convection-diffusion problems. CMES: Computer Modeling in Engineering & Sciences, vol. 1, pp. 45-60.
20. Lin, H.; Atluri, S. N. (2001): The Meshless Local Petrov-Galerkin (MLPG) method for solving incompressible Navier-Stokes equations. CMES: Computer Modeling in Engineering & Sciences, vol. 2, pp. 117-142. (Pubitemid 33626565)
21. Metcalfe, G.; Lester, D.; Ord, A.; Kulkarni, P.; Rudman, M.; Trefry, M.; Hobbs, B.; Regenaur-Lieb, K.; Morris, J. (2010): An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow. Proc. R. Soc. Lond. A, vol. 368, pp. 2147-2162.
22. Patankar, S. V. (1980): Numerical heat transfer and fluid flow. Hemisphere Publishing Co.
23. Price, T. J.; Mullin, T.; Kobine, J. J. (2003): Numerical and experimental characterization of a family of two-roll-mill flows. Proc. R. Soc. Lond. A, vol. 459, pp. 117-135. (Pubitemid 38315497)
24. Shankar, P. N.; Kidambi, R. (2009): Mixing in internally stirred flows. Proc. R. Soc. Lond. A, vol. 465, pp. 1271-1290.
25. Spalding, D. B. (1972): A novel finite difference formulation for differential expressions involving both first and second derivatives. International Journal for Numerical Methods in Engineering, vol. 4, pp. 551-559.
26. Stremler, M. A.; Haselton, F. R.; Aref, H. (2004): Designing for chaos: applications of chaotic advection at the microscale. Phil. Trans. R. Soc. Lond. A., vol. 362, pp. 1019-1036. (Pubitemid 38652645)
27. Wang, J.; Feng, L.; Otino, J. M.; Lueptow, R. (2009): Inertial effects on chaotic advection and mixing in a 2D cavity flow. Ind. Eng. Chem. Res., vol. 48, pp. 2436-2442.
28. Ying, L. A.; Atluri, S. N. (1983): A Hybrid finite element method for Stokes flow: Part II-stability and convergence studies. Computer Methods in Applied Mechanics and Engineering, vol. 36, pp. 39-60. (Pubitemid 13487941)
29. Zhu, T.; Zhang, J. D.; Atluri, S. N. (1998): A local boundary integral (LBIE) method in computational mechanics, and a meshless discretization approach. Computational Mechanics, vol. 21, pp. 223-235. (Pubitemid 128566412)