A Multidomain Chebyshev Pseudo-Spectral Method for Fluid Flow and Heat Transfer from Square Cylinders

REFERENCES

• H. J. H. Clercx, A Spectral Solver for the Navier-Stokes Equations in the Velocity-Vorticity Formulation for Flows with Two Nonperiodic Directions, J. Comput. Phys., vol. 137, pp. 186–211, 1997.
   Web of Science ®Google Scholar
• J. Li and W. W. Sun, Spectral Method of Decoupling the Vorticity, and Stream Function for the Incompressible Fluid Flows, Comput. Math. Appl., vol. 37, pp. 35–40, 1999.
   Web of Science ®Google Scholar
• R. Peyret, Spectral Methods for the Vorticity-Streamfunction Equations, Comput. Fluids Dynam. Rev., pp. 395–417, 1998.
   Google Scholar
• C. H. Zhang, W. Zhang, and G. Xi, A Pseudospectral Multidomain Method for Conjugate Conduction-Convection in Enclosures, Numer. Heat Transfer B, vol. 57, pp. 260–282, 2010.
   Web of Science ®Google Scholar
• C. Bernardi and Y. Maday, A Collocation Method over Staggered Grids for the Stokes Problem, Int. J. Numer. Meth. Fluids, vol. 8, pp. 537–577, 1988.
   Web of Science ®Google Scholar
• F. Montigny-Rannou and Y. Morchoisne, A Spectral Method with Staggered Grid for Incompressible Navier-Stokes Equations, Int. J. Numer. Meth. Fluids, vol. 7, pp. 175–189, 1987.
   Web of Science ®Google Scholar
• M. R. Schumack, W. W. Schultz, and J. P. Boyd, Spectral Method Solution of the Stokes Equations on Nonstaggered Grids, J. Comput. Phys., vol. 94, pp. 30–58, 1991.
   Web of Science ®Google Scholar
• O. Botella, On the Solution of the Naiver-Stokes Equations Using Chebyshev Projection Schemes with Third-Order Accuracy in Time, Comput. Fluids, vol. 26, no.2, pp. 107–116, 1997.
   Web of Science ®Google Scholar
• O. Botella and R. Peyret, Benchmark Spectral Results on the Lid-Driven Cavity Flow, Comput. Fluids, vol. 27, no.4, pp. 421–433, 1998.
   Web of Science ®Google Scholar
• W. Zhang, C. H. Zhang, and G. Xi, An Explicit Chebyshev Pseudospectral Mulitgrid Method for Incompressible Navier-Stokes Equations, Comput. Fluids, vol. 39, no.1), pp. 178–188, 2010.
   Web of Science ®Google Scholar
• W. Zhang, G. Xi, C. H. Zhang, and Z. Huang, A High-Accuracy Temporal-Spatial Pesudospectral Method for Time-Periodic Unsteady Fluid Flow and Heat Transfer Problems, Int. J. Comput. Fluid Dynam., vol. 25, no. 4, pp. 191–206, 2011.
   Web of Science ®Google Scholar
• W. Zhang, C. H. Zhang, and G. Xi, Conjugate Conduction-Natural Convection in an Enclosure with Time-Periodic Sidewall Temperature and Inclination, Int. J. Heat Fluid Flow, vol. 32, pp. 52–62, 2011.
   Web of Science ®Google Scholar
• W. Zhang, Z. Huang, C. H. Zhang, and G. Xi, Conjugate Wall Conduction-Fluid Natural Convection in a Three-Dimensional Inclined Enclosure, Numer. Heat Transfer A, vol. 61, pp. 122–141, 2012.
   Web of Science ®Google Scholar
• W. Zhang, Z. Huang, C. H. Zhang, and G. Xi, Numerical Study on Conjugate Conduction-Convection in a Cubic Enclosure Submitted to Time-Periodic Sidewall Temperature, ASME J. Heat Transfer, vol. 135, pp. 022504–022504-10, 2012.
   Google Scholar
• Z. Huang, W. Zhang, and G. Xi, Natural Convection Heat Transfer in a Cubic Cavity Submitted to Time-Periodic Sidewall Temperature, Numer. Heat Transfer A, vol. 67, pp. 13–32, 2015.
   Web of Science ®Google Scholar
• Z. Huang, W. Zhang, and G. Xi, Numerical Simulation of Time-Periodic Natural Convection in Inclined 2D/3D Cavity. The 4th Symposium on Computational Heat Transfer and Fluid Flow, Hong Kong, ASCHT-T01–1-A, 2013.
   Google Scholar
• H. H. Yang and B. Shizgal, Chebyshev Pseudospectral Multi-domain Technique for Viscous Flow Calculation, Comput. Meth. Appl. Mech. Eng., vol. 118, pp. 47–61, 1994.
   Web of Science ®Google Scholar
• C. Sabbah and R. Pasquetti, A Divergence-Free Multidomain Spectral Solver of the Navier-Sokes Equaitons in Geometries of High Aspect Ratio, J. Comput. Phys., vol. 139, pp. 359–379, 1998.
   Web of Science ®Google Scholar
• M. Deville, L. Kleiser, and F. Montigny-Rannou, Pressure and Time Treatment for Chebyshev Spectral Solution of a Stokes Equations, Int. J. Numer. Meth. Fluids, vol. 4, pp. 1149–1163, 1984.
   Google Scholar
• A. J. Chorin, Numerical Solution of the Navier-Stokes Equations, Math. Comput., vol. 22, pp. 745–762, 1968.
   Web of Science ®Google Scholar
• R. Temam, Une methode d’approximation de la solution des equations de Navier-Stokes, Bull. Soc. Math. France, vol. 96, pp. 115–152, 1968.
   Web of Science ®Google Scholar
• J. Kim and P. Moin, Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations, J. Comput. Phys., vol. 59, pp. 308–323, 1985.
   Web of Science ®Google Scholar
• J. J. Martinez, and P. T. T. Esperanca, A Chebyshev Collocation Spectral Method for Numerical Simulation of Incompressible flow Problems, J. Braz. Soc. Mech. Sci. Eng., vol. 29, pp. 317–328, 2007.
   Web of Science ®Google Scholar
• D. Gottlieb, M. Y. Hussaini, and S. A. Orszag, Theory and Applications of Spectral Methods, Proceedings of the Spectral Methods Conference for PDE’s, SIAM, pp.1–54, 1984.
   Google Scholar
• A. Bayliss, A. Class, and B. J. Matkowsky, Roundoff Error in Computing Derivatives Using the Chebyshev Differentiation Matrix, J. Comput. Phys., vol. 116, pp. 380–383, 1995.
   Web of Science ®Google Scholar
• R. Peyret Spectral Method for Incompressible Viscous Flow, Springer-Verlag, New York, 2002.
   Google Scholar
• Z. Huang, G. Xi, W. Zhang, and S. P. Wen, Mixed Convection Heat Transfer from Confined Tandem Square Cylinders in a Horizontal Channel, Int. J. Heat Mass Transfer, vol. 66, pp. 625–631, 2013.
   Web of Science ®Google Scholar
• Z. Huang, G. Xi, and W. Zhang, Numerical Simulation of Spacing Effects on the Flow Past Two 2:1 Rectangular Cylinders in Tandem at Re = 200, Proceedings of the ASME 2012 Fluids Engineering Summer Meeting, Puerto Rico, FEDSM2012–72157, 2012.
   Google Scholar
• G. de Vahl Davis, Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution, Int. J. Numer. Meth. Fluids, vol. 3, pp. 249–264, 1983.
   Web of Science ®Google Scholar
• P. L. Quere and T. A. D. Roquefort, Computation of Natural Convection in Two-Dimensional Cavities with Chebyshev Polynomials, J. Comput. Phys., vol. 57, pp. 210–228, 1985.
   Web of Science ®Google Scholar
• B. Paliwal, A. Sharma, R. P. Chhabra, and V. Eswaran, Power Law Fluid Flow past a Square Cylinder: Momentum and Heat Transfer Characteristics, Chem. Eng. Sci., vol. 58, pp. 5315–5329, 2003.
   Web of Science ®Google Scholar
• A. K. Dhiman, R. P. Chhabra, and V. Eswaran, Heat Transfer to Power-Law Fluids from a Heated Square Cylinder, Numer. Heat Transfer A, vol. 52, pp. 185–201, 2007.
   Web of Science ®Google Scholar
• A. Sohankar and A. Etminan, Forced-Convection Heat Transfer from Tandem Square Cylinders in Cross Flow at Low Reynolds Numbers, Int. J. Numer. Meth. Fluids, vol. 60, pp. 733–751, 2009.
   Web of Science ®Google Scholar
• A. Sohankar, C. Norberg, and L. Davidson, Low-Reynolds-Number Flow around a Square Cylinder at Incidence: Study of Blockage, Onset of Vortex Shedding and Outlet Boundary Condition, Int. J. Numer. Meth. Fluids, vol. 26, pp. 39–56, 1998.
   Web of Science ®Google Scholar
• A. Sohankar, C. Norberg, and L. Davidson, Numerical Simulation of Unsteady Low-Reynolds Number Flow around Rectangular Cylinders at Incidence, J. Wind Eng. Ind. Aerodynam., vol. 69–71, pp. 189–201, 1997.
   Web of Science ®Google Scholar
• D. Chatterjee and S. Amiroudine, Two-Dimensional Mixed Convection Heat Transfer from Confined Tandem Square Cylinders in Cross-Flow at Low Reynolds Numbers, Int. Commun. Heat Mass Transfer, vol. 37, pp. 7–16, 2010.
   Web of Science ®Google Scholar