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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 62, 2012 - Issue 5
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Original Articles

Grid-Free Vortex Methods for Natural Convection; Handling Source Terms and Nonlinear Diffusion

Pages 370-398 | Received 02 May 2012, Accepted 11 Jun 2012, Published online: 27 Sep 2012

REFERENCES

  • N. N. Abdelmalek , Minimum l [Infinity] Solution of Underdetermined Systems of Linear Equations , J. Approx. Theory , vol. 20 , no. 1 , pp. 57 – 69 , 1977 .
  • C. R. Anderson and M. B. Reider , A High Order Explicit Method for the Computation of Flow about a Circular Cylinder, J. Comput. Phys. , vol. 125, pp. 207–224, 1996.
  • L. A. Barba , A. Leonard , and C. B. Allen , Vortex Method with Meshless Spatial Adaption for Accurate Simulation of Viscous, Unsteady Vortical Flows , Int. J. Numer. Meth. Fluids , vol. 47 , pp. 841 – 848 , 2005 .
  • J. E. Barnes and P. Hut , A Hierarchical o(nlogn) Force Calculations Algorithm , Nature , vol. 324 , p. 446 , 1986 .
  • J. T. Beale and A. Majda , High Order Accurate Vortex Methods with Explicit Velocity Kernels , J. Comput. Phys. , vol. 58 , pp. 188 – 208 , 1985 .
  • R. Bouard and M. Coutanceau , The Early Stage of Development of the Wake behind an Impulsively Started Cylinder for 40 < Re < 104 , J. Fluid Mech. , vol. 101 , pp. 583 – 607 , 1980 .
  • C. P. Brescianini and M. A. Delichatsios , New Evaluation of the k-ε Turbulence Model for Free Buoyant Plumes , Numerical Heat Transfer A , vol. 43 , pp. 731 – 751 , 2003 .
  • D. Calvetti , G. Landi , L. Reichel , and F. Sgallari , Non-negativity and Iterative Methods for Ill-Posed Problems , Inverse Prob. , vol. 20 , pp. 1747 – 1758 , 2004 .
  • A. J. Chorin , Numerical Study of Slightly Viscous Flow , J. Fluid Mech. , vol. 57 , pp. 785 – 796 , 1973 .
  • A. J. Chorin , Vortex Methods, PAM Report 593, Department of Mahematics, University of California, Berkeley, CA, 1993.
  • G.-H. Cottet and P. Koumoutsakos , Vortex Methods: Theory and Applications , Cambridge University Press , Cambridge , UK , 2000 .
  • G.-H. Cottet , P. Koumoutsakos , and M. Lemine Ould Salihi , Vortex Methods with Spatially Varying Cores , J. Comput. Phys. , vol. 162 , pp. 164 – 185 , 2000 .
  • Y. H. Dai and Y. Yuan , A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property , SIAM J. Optimization , vol. 10 , no. 1 , pp. 177 – 182 , 2000 .
  • M. Darwish , I. Sraj , and F. Moukalled , A Coupled Incompressible Flow Solver on Structured Grids , Numer. Heat Transfer B , vol. 52 , pp. 353 – 371 , 2007 .
  • P. Degond and S. Mas-Gallic , The Weighted Particle Method for Convection-Diffusion Equations, Part 2: The Anisotropic Case , Math. Comput. , vol. 53 , pp. 509 – 525 , 1989 .
  • A. A. Dehghan , and M. Khoshab , Numerical Simulation of Buoyancy-Induced Turbulent Flow between Two Concentric Isothermal Spheres , Heat Transfer Eng. , vol. 31 , no. 1 , pp. 33 – 44 , 2010 .
  • J. D. Eldredge , T. Colonius , and A. Leonard , A Vortex Particle Method for Two-Dimensional Compressible Flow , J. Comput. Phys. , vol. 179 , pp. 371 – 399 , 2002 .
  • R. Fletcher , Conjugate Gradient Methods for Indefinite Systems, G. A. Watson, Editor, pp. 73–89. Proceedings of the Dundee Biennal Conference on Numerical Analysis, 1974, Springer-Verlag, New York 1975.
  • R. Fletcher and M. J. D. Powell , A Rapidly Convergent Descent Method for Minimization , Comput. J. , vol. 6 , no. 2 , p. 163 , 1963 .
  • A. F. Ghoniem , I. Lakkis , and M. Soteriou , Numerical Simulation of the Dynamics of Large Fire Plumes and the Phenomenon of Puffing , 26th Symp. (Int.) on Combustion, pp. 1531–1539, The Combustion Institute, Pittsburgh, PA, 1996.
  • A. F. Ghoniem and O. M. Knio , The Development and Application of the Transport Element Method to Three Dimensional Reacting Shear Layers , Vortex Dynam. Vortex Meth. , vol. 28 , p. 165 , 1991 .
  • L. Greengard and V. Rohklin , A Fast Algorithm for Particle Simulations , J. Comput. Phys. , vol. 73 , p. 325 , 1987 .
  • W. W. Hager and H. Zhang , A Survey of Nonlinear Conjugate Gradient Methods , Pacific J. Optimization , vol. 2 , pp. 35 – 58 , 2006 .
  • B. K. Hakizumwami , High Reynolds Number Flow past an Impulsively Started Circular Cylinder , Comput. Fluids , vol. 23 , pp. 895 – 902 , 1994 .
  • M. R. Hestenes and E. Stiefel , Methods of Conjugate Gradients for Solving Linear Systems, J. Res. Natl. Bur. of Std. , vol. 49, no. 6, pp. 409–436, 1952.
  • J. Honerkamp and J. Weese , Tikhonovs Regularization Method for Ill-Posed Problems , Continuum Mech. Thermodynam. , vol. 2 , no. 1 , pp. 17 – 30 , 1990 .
  • O. Knio and A. Ghoniem , Vortex Simulation of a Three-Dimensional Reacting Shear Layer with Infinite-Rate Kinetics , AIAA J. , vol. 30 , no. 1 , pp. 105 – 116 , 1992 .
  • P. Koumoutsakos and A. Leonard , High-Resolution Simulations of the Flow around an Impulsively Started Cylinder Using Vortex Methods , J. Fluid Mech. , vol. 296 , pp. 1 – 38 , 1995 .
  • A. Krishnan and A. F. Ghoniem , Simulation of Rollup and Mixing in Rayleigh-Taylor Flow Using the Transport-Element Method , J. Comput. Phys. , vol. 99 , pp. 1 – 27 , 1992 .
  • K. Kuwahara and H. Takami , Numerical Studies of Two-Dimensional Vortex Motion by a System of Point Vortices , J. Phys. Soc. of Japan , vol. 34 , no. 1 , pp. 247 – 253 , 1973 .
  • I. Lakkis and A. F. Ghoniem , Lagrangian Simulation of Fire Plumes , 7th AIAA/ASME Joint Thermodynamics and Heat Transfer Conf. , vol. 1 , pp. 215 – 226 , 1998 .
  • I. Lakkis and A. F. Ghoniem , Grid-Free Simulation of Radiative Transport in a Participating Medium, ESAIM: Proceedings, vol. 7, pp. 234–246. edpsciences. org, 1999.
  • I. Lakkis and F. Moukalled , Natural-Convection Heat Transfer in Channels with Isothermally Heated Convex Surfaces , Numer. Heat Transfer A , vol. 53 , pp. 1176 – 1194 , 2008 .
  • I. A. Lakkis and A. F. Ghoniem , Grid-Free Simulation of a Reacting Radiating Fuel Ring, AIAA, Aerospace Sciences Meeting and Exhibit, 38th, Reno, NV, 2000.
  • I. Lakkis and A. Ghoniem , Axisymmetric Vortex Method for Low-Mach Number, Diffusion-Controlled Combustion , J. Comput. Phys. , vol. 182 , pp. 435 – 475 , 2003 .
  • I. Lakkis and A. Ghoniem , A High Resolution Spatially Adaptive Vortex Method for Separating Flows. Part I: Two-Dimensional Domains , J. Comput. Phys. , vol. 228 , pp. 491 – 515 , 2009 .
  • C. Lanczos , Solution of Systems of Linear Equations by Minimized Iterations , J. Res. Natl. Bur. Sta. , vol. 49 , no. 1 , pp. 33 – 53 , 1952 .
  • C. L. Lawson and R. J. Hanson , Solving Least Squares Problems. Society for Industrial Mathematics , 1987 .
  • A. Leonard , Vortex Methods for Flow Simulation , J. Comput. Phys. , vol. 37 , pp. 289 – 335 , 1980 .
  • A. Leonard , D. Shiels , J. K. Salmon , G. S. Winckelmans , and P. Ploumhans , Recent Advances in High Resolution Vortex Methods for Incompressible Flows , 13th AIAA Computational Fluid Dynamics Conf. , vol. 97 , p. 2108 , June 29–July 2, 1997 .
  • T. P. Loc , Numerical Analysis of Unsteady Secondary Vortices Generated by an Impulsively Started Circular Cylinder , J. Fluid Mech. , vol. 100 , pp. 111 – 128 , 2006 .
  • A. Majda and K. G. Lamb , Simplified Equations for Low Mach Number Combustion with Strong Heat Release , Dynam. Issues Combustion Theory , vol. 35 , pp. 167 – 211 , 1991 .
  • A. Majda and J. Sethian , Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion , Combustion Sci. Technol , vol. 42 , no. 3–4 , pp. 185 – 205 , 1985 .
  • J. S. Marshall and J. R. Grant , Penetration of a Blade into a Vortex Core: Vorticity Response and Unsteady Blade Forces , J. Fluid Mech. Digital Archive , vol. 306 , pp. 83 – 109 , 1996 .
  • H. N. Najm , R. B. Milne , K. D. Devine , and S. N. Kempka , A Coupled Lagrangian-Eulerian Scheme for Reacting Flow Modeling , ESAIM: Proceedings , vol. 7 , pp. 304 – 313 . edpsciences. org, 1999.
  • J. A. Nelder and R. Mead , A SIMPLEX Method for Function Minimization , Comput. J. , vol. 7 , no. 4 , p. 308 , 1965 .
  • F. M. Pepin , Simulation of the Flow past an Impulsively Started Cylinder Using a Discrete Vortex Method. Ph.D. thesis, California Institute of Technology, Rwadena, CA, 1990.
  • P. Ploumhans and G. S. Winckelmans , Vortex Methods for High-Resolution Simulations of Viscous Flow past Bluff Bodies of General Geometry, J. Comput. Phys. , vol. 165, pp. 354–406, 2000.
  • J. Ray , H. N. Najm , R. B. Milne , K. D. Devine , and S. Kempka , Triple Flame Structure and Dynamics at the Stabilization Point of an Unsteady Lifted Jet Diffusion Flame , Proceedings-Combustion Inst. , vol. 28 , no. 1 , pp. 219 – 226 , 2000 .
  • J. B. Rosen , The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints , J. SIAM J. , vol. 8 , no. 1 , pp. 181 – 217 , 1960 .
  • R. Roslan , H. Saleh , and I. Hashim , Buoyancy-Driven Heat Transfer in Nanofluid-Filled Trapezoidal Enclosure with Variable Thermal Conductivity and Viscosity , Numer. Heat Transfer A. , vol. 60 , pp. 867 – 882 , 2011 .
  • L. F. Rossi , Resurrecting Core Spreading Vortex Methods: A New Scheme That Is Both Deterministic and Convergent , SIAM J. Sci. Comput. , vol. 17 , no. 2 , pp. 370 – 397 , 1996 .
  • Y. Saad , A Flexible Inner-Outer Preconditioned GMRES Algorithm , SIAM J. Sci. Comput. , vol. 14 , pp. 461 – 461 , 1993 .
  • Y. Saad and M. H. Schultz , GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems , SIAM J. Sci. Stat. Comput. , vol. 7 , no. 3 , pp. 856 – 869 , 1986 .
  • I. F. Sbalzarini , J. H. Walther , M. Bergdorf , S. E. Hieber , E. M. Kotsalis , and P. Koumoutsakos , PPM—A Highly Efficient Parallel Particle–Mesh Library for the Simulation of Continuum Systems , J. Comput. Phys. , vol. 215 , pp. 566 – 588 , 2006 .
  • F. Schlegel , D. Wee , and A. F. Ghoniem , A Fast 3D Particle Method for the Simulation of Buoyant Flow , J. Comput. Phys. , vol. 227 , pp. 9063 – 9090 , 2008 .
  • N. Sekarapandian , Y. Sanyasiraju , and S. Vengadesan , A Novel Semi-explicit Spatially Fourth Order Accurate Projection Method for Unsteady Incompressible Viscous Flows , Numer. Heat Transfer A , vol. 56 , pp. 665 – 684 , 2009 .
  • S. Shankar and L. Dommelen , A New Diffusion Procedure for Vortex Methods , J. Comput. Phys. , vol. 127 , pp. 88 – 109 , 1996 .
  • J. R. Shewchuk , An Introduction to the Conjugate Gradient Method without the Agonizing Pain, Technical Report, Carnegie Mellon University, Pittsburgh, PA, 1994 .
  • M. C. Soteriou and A. F. Ghoniem , Numerical Simulation of Unsteady Combustion Using the Transport Element Method , ESAIM: Proceedings , vol. 1 , pp. 429 – 446 . Citeseer, 1996.
  • S. Subramaniam , A New Mesh-Free Vortex Method. Ph.D. Thesis, Florida State University, 1996.
  • A. N. Tikhonov , Solution of Incorrectly Formulated Problems and the Regularization Method , Sov. Math. Dokl. , vol. 4 , pp. 1035 – 1038 , 1963 .
  • G. W. Kruse and P. Fischer , Private communication, Center for Fluid Mechanics, Brown University, Providence, RI, 1996.

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