Spectral Fourier–Galerkin benchmark solution for natural convection in an inclined saturated porous medium

References

• D. A. Nield, and A. Bejan, Convection in Porous Media, 3rd ed., Springer, New York, NY, 2006.
   Google Scholar
• D. B. Ingham and I. Pop, eds. Transport Phenomena in Porous Media, Elsevier, Oxford, UK, 2005.
   Google Scholar
• K. Vafai, ed., Handbook of Porous Media, 2nd ed., Taylor & Francis, Boca Raton, FL, 2005.
   Google Scholar
• M. J. S. de Lemos, Turbulence in Porous Media: Modeling and Applications, Elsevier, Oxford, UK, 2006.
   Google Scholar
• P. Vadasz, ed., Emerging Topics in Heat and Mass Transfer in Porous Media, Springer, New York, NY, 2008.
   Google Scholar
• P. Vadasz, Bifurcation Phenomena in Natural Convection in Porous Media, Heat Transfer, vol. 5, pp. 147–152, Hemisphere, Washington, DC, 1990.
   Google Scholar
• B. Goyeau, J. P. Songbe, and D. Gobin, Numerical Study of Double-Diffusive Natural Convection in a Porous Cavity Using the Darcy-Brinkman Formulation, Int. J. Heat Mass Transf., vol. 39, pp. 1363–1378, 1996.
   Web of Science ®Google Scholar
• D. M. Manole and J. L. Lage, Numerical Benchmark Results for Natural Convection in a Porous Medium Cavity, Heat and Mass Transfer in Porous Media, ASME Conf., HTD-vol. 216, pp. 55–60, 1992.
   Google Scholar
• R. J. Gross, M. R. Bear, and C. E. Hickox, The Application of Flux Corrected Transport (FCT) to High Rayleigh Number Natural Convection in a Porous Medium, Proceedings of 8th International on Heat Transfer Conference, San Francisco, CA, 1986.
   Google Scholar
• N. H. Saeid and I. Pop, Natural Convection from a Discrete Heater in a Square Cavity Filled with a Porous Medium, J. Porous Media, vol. 8, pp. 55–63, 2005.
   Web of Science ®Google Scholar
• A. C. Baytas and I. Pop, Free Convection in a Square Porous Cavity Using a Thermal Non-Equilibrium Model, Int. J. Thermal Sci., vol. 41, pp. 861–870, 2002.
   Web of Science ®Google Scholar
• A. Bejan, On the Boundary Layer Regime in a Vertical Enclosure Filled with a Porous Medium, Lett. Heat Mass Transf., vol. 6, pp.93–102, 1979.
   Web of Science ®Google Scholar
• E. V. Kalabin, M. V. Kanashina, and P. T. Zubkov, Natural-Convective Heat Transfer in a Square Cavity with Time-Varying Side-Wall Temperature, Numerical Heat Transfer A, vol. 47, no. 6, pp. 621–631, 2005.
   Web of Science ®Google Scholar
• Rathnam, V. Mani, P. Biswal, and T. Basak, Analysis of Entropy Generation During Natural Convection Within Entrapped Porous Triangular Cavities During Hot or Cold Fluid Disposal, Numerical Heat Transfer, Part A: Applications, vol. 69, no. 9, pp. 931–956, 2016.
   Web of Science ®Google Scholar
• V. Prasad and F. A. Kulacki, Convective Heat Transfer in a Rectangular Porous Cavity-Effect of Aspect Ratio on Flow Structure and Heat Transfer, J. Heat Transfer, vol. 106, pp. 158–165, 1984.
   Web of Science ®Google Scholar
• V. Prasad and A. Tuntomo, Inertia Effects on Natural Convection in a Vertical Porous Cavity, Numerical Heat Transfer B, vol. 11, pp. 295–320, 1987.
   Web of Science ®Google Scholar
• A. C. Baytas, Entropy Generation for Natural Convection in an Inclined Porous Cavity, International Journal of Heat and Mass Transfer, vol. 43, no. 12, pp. 2089–2099, 2000.
   Web of Science ®Google Scholar
• Zargartalebi, Hossein, et al. “Natural Convection of a Nanofluid in an Enclosure with an Inclined Local Thermal Non-Equilibrium Porous Fin Considering Buongiorno’s Model, Numerical Heat Transfer, Part A, vol. 70, no. 4, pp. 432–445, 2016.
   Web of Science ®Google Scholar
• A. J. Chamkha and A. Al-Mudhaf, Double-Diffusive Natural Convection in Inclined Porous Cavities with Various Aspect Ratios and Temperature-Dependent Heat Source or Sink, Heat and Mass Transfer/Waerme-und Stoffuebertragung, vol. 44, no. 6, pp. 679–693, 2008.
   Web of Science ®Google Scholar
• J. Rasoul and P. Prinos, Natural Convection in an Inclined Enclosure, International Journal of Numerical Methods for Heat and Fluid Flow, vol. 7, no. 5, pp. 438–478, 1997.
   Web of Science ®Google Scholar
• O. Aydin, A. Unal, and T. Ayhan, A Numerical Study on Buoyancy-Driven Flow in an Inclined Square Enclosure Heated and Cooled on Adjacent Walls, Numer. Heat Transf., Part A, vol. 36, pp. 585–599, 1999.
   Web of Science ®Google Scholar
• M. Rahman and M. A. R. Sharif, Numerical Study of Laminar Natural Convection in Inclined Rectangular Enclosures of Various Aspect Ratios, Numer. Heat Transf. Part A, vol. 44, pp. 355–373, 2003.
   Web of Science ®Google Scholar
• A. C. Baytas, I. Pop, Free convection in oblique enclosures filled with a porous medium, Int. J. Heat Mass transfer 42, 1999.
   Web of Science ®Google Scholar
• C. G. Broyden, A Class of Methods for Solving Nonlinear Simultaneous Equations, Math. Comput. J., vol. 19, pp. 577–593, 1965.
   Web of Science ®Google Scholar
• A. Younes and M. Fahs, A Semi-Analytical Solution for the Reactive Henry Saltwater Intrusion Problem, Water, Air, & Soil Pollution, vol. 224, pp. 1779, 2013.
   Web of Science ®Google Scholar
• L. S. de B. Alves and R. M. Cotta, Transient Natural Convection Inside Porous Cavities: Hybrid Numerical-Analytical Solution and Mixed Symbolic-Numerical Computation, Numer. Heat Transfer A, vol. 38, pp. 89–110, 2000.
   Web of Science ®Google Scholar
• A. Zidane, A. Younes, P. Huggenberger, and E. Zechner, The Henry Semi-Analytical Solution for Saltwater Intrusion with Reduced Dispersion, Water Resources Res., vol. 48, pp. 1–10, 2012.
   Web of Science ®Google Scholar
• H. S. Nawaf and I. Pop, Transient Free Convection in a Square Cavity Filled with a Porous Medium, Int. J. Heat Mass Transfer, vol. 47, pp. 1917–1924, 2004.
   Web of Science ®Google Scholar
• S., Qian, M. Fahs, et al. A High-Accurate Solution for Darcy-Brinkman Double-Diffusive Convection in Saturated Porous Media, Numerical Heat Transfer, Part B, vol. 69, no. 1, pp. 26–47, 2016.
   Web of Science ®Google Scholar
• M. Fahs and A. Younes, A High Accurate Fourier-Galerkin Solution for Buoyancy-Driven Flow in a Square Cavity, Numer. Heat Transfer B, vol. 65, pp. 495–517, 2014.
   Web of Science ®Google Scholar
• D. Durran, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics, Chap. 4, Springer-Verlag, New York, NY, 1999.
   Google Scholar
• B. Costa, Spectral Methods for Partial Differential Equations, Cubo Math. J., vol. 6, pp. 1–32, 2004.
   Google Scholar
• M. A. Christou and C. I. Christov, Localized Waves for the Regularized Long Wave Equation via a Galerkin Spectral Method, Math. Comput. Simul., vol. 69, pp. 257–268, 2005.
   Web of Science ®Google Scholar
• C. Canuto, M. Hussaini, A. Quarteroni, and T. Zang, Spectral Methods: Fundamentals in Single Domains, Chap. 3, Springer-Verlag, New York, 2006.
   Google Scholar
• D. A. Kopriva, Implementing Spectral Methods for Partial Differential Equations, Chap. 4, Springer Science, New York, 2009.
   Google Scholar
• M. Y. Hussaini and T. A. Zang, Spectral Methods in Fluid Dynamics, Annu. Rev. Fluid Mech., vol. 19, pp. 339–367, 1987.
   Web of Science ®Google Scholar
• M. Christou and C. I. Christov, Fourier–Galerkin Method for Localized Solutions of Equations with Cubic Nonlinearity, J. Comput. Anal. Appl., vol. 4, pp. 63–77, 2002.
   Web of Science ®Google Scholar
• M. A. Christou and C. I. Christov, Fourier–Galerkin Method for Interacting Localized Waves, J. Neural Parallel Sci. Comput., vol. 4, pp. 63–77, 2002.
   Google Scholar
• M. Christou and C. I. Christov, Fourier–Galerkin Method for 2D Solutions of Boussinesq Equation, Math. Comput. Simul., vol. 74, pp. 82–92, 2007.
   Web of Science ®Google Scholar
• K. Hooman, Heat and Fluid Flow in a Rectangular Microchannel Filled with a Porous Medium, Int. J. Heat Mass Transfer, vol. 51, pp. 5804–5810, 2008.
   Web of Science ®Google Scholar
• S. Mahmud and I. Pop, Mixed Convection in a Square Vented Enclosure Filled with a Porous Medium, Int. J. Heat Mass Transfer, vol. 49, pp. 2190–2206, 2006.
   Web of Science ®Google Scholar
• MINPACK, Math = Library, Jorge More, Burton Garbow, University of Chicago, the Department of Energy (DOE), Argonne National Laboratory, 1980.
   Google Scholar
• W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3d ed., Chapters 9–10, Cambridge University Press, New York, NY, 2007.
   Google Scholar
• M. J. D. Powell, An Efficient Method for Finding the Minimum of a Function of Several Variables Without Calculating Derivatives, Comput. J., vol. 7, pp. 155–162, 1964.
   Web of Science ®Google Scholar
• M. J. D. Powell, On the Calculations of Orthogonal Vectors, Comput. J., vol. 1, pp. 302–304, 1968.
   Web of Science ®Google Scholar
• R. Rajamani, C. Srinivas, and K. N. Seetharamu, Finite Element Analysis of Convection Heat Transfer in Porous Media, Int. J. Numer. Meth. Fluids, vol. 11, pp. 331–339, 1990.
   Web of Science ®Google Scholar
• D. Misra and A. Sarkar, A Comparative Study of Porous Media Models in a Differentially Heated Square Cavity Using a Finite Element Method, Int. J. Numer. Meth. Heat Fluid Flow, vol. 5, pp. 735–752, 1995.
   Web of Science ®Google Scholar
• A. Younes, M. Fahs, and S. Ahmed, Solving Density Driven Flow Problems with Efficient Spatial Discretizations and Higher-Order Time Integration Methods, Adv. Water Res., vol. 32, pp. 340–352, 2009.
   Web of Science ®Google Scholar
• K. L. Walker and G. M. Homsy, Convection in a Porous Cavity, J. Fluid Mech., vol. 87, pp. 449–474, 1978.
   Web of Science ®Google Scholar