A novel immersed boundary/Fourier pseudospectral method for flows with thermal effects

References

• N. Kazuhiro, I. Yasushi, and T. Fumiya, Some Challenges of Realistic Flow Simulations by Unstructured Grid CFD, Int. J. Numer. Meth. Fluids, vol. 43, pp. 769–783, 2003.
   Web of Science ®Google Scholar
• C. Peskin, Flow Patterns around Heart Valves: A Numerical Method, J. Comput. Phys., vol. 10, pp. 252–271, 1972.
   Web of Science ®Google Scholar
• D. Goldstein, R. Handler, and L. Sirovich, Modeling a No-Slip Flow Boundary with an External Force Field, J. Comput. Phys., vol. 105, pp. 354–366, 1993.
   Web of Science ®Google Scholar
• A. L. L. e Silva, A. Silveira-Neto, and J. Damasceno, Numerical Simulation of Two-Dimensional Flows over a Circular Cylinder Using the Immersed Boundary Method, J. Comput. Phys., vol. 189, pp. 351–370, 2003.
   Web of Science ®Google Scholar
• F. Mariano, L. Moreira, A. Silveira-Neto, C. B. da Silva, and J. Pereira, A New Incompressible Navier-Stokes Solver Combining Fourier Pseudo-Spectral and Immersed Boundary Method, CMES: Comput. Model. Eng. Sci., vol. 59, pp. 181–216, 2010.
   Web of Science ®Google Scholar
• O. Botella and R. Peyret, Benchmark Spectral Results on the Lid-Driven Cavity Flow, Computers Fluids, vol. 27, pp. 421–433, 1998.
   Web of Science ®Google Scholar
• H. Jeong, H. Yoon, M. Ha, and M. Tsutahara, An Immersed Boundary-Thermal Lattice Boltzmann Method Using an Equilibrium Internal Energy Density Approach for the Simulation of Flows with Heat Transfer, J. Comput. Phys., vol. 229, pp. 2526–2543, 2010.
   Web of Science ®Google Scholar
• Z. Wang, J. Fan, K. Luo, and K. Cen, Immersed Boundary Method for the Simulation of Flows with Heat Transfer, Int. J. Heat Mass Transfer, vol. 52, pp. 4510–4518, 2009.
   Web of Science ®Google Scholar
• N. Zhang, Z. Zheng, and S. Eckels, Study of Heat-Transfer on the Surface of a Circular Cylinder in Flow Using an Immersed-Boundary Method, Int. J. Heat Fluid Flow, vol. 29, pp. 1558–1566, 2008.
   Web of Science ®Google Scholar
• W. Ren, C. Shu, and W. Yang, Boundary Condition-Enforced Immersed Boundary Method for Thermal Flow Problems with Dirichlet Temperature Condition and Its Applications, Computers Fluids, vol. 57, pp. 40–51, 2012.
   Web of Science ®Google Scholar
• J. Pacheco, A. Pacheco-Vega, T. Rodić, and R. Peck, Numerical Simulations of Heat Transfer and Fluid Flow Problems Using an Immersed-Boundary Finite-Volume Method on Nonstaggered Grids, Numer. Heat Transfer B, vol. 48, pp. 1–24, 2005.
   Web of Science ®Google Scholar
• C. Canuto, M. Hussaini, A. Quarteroni, and T. Zang, Spectral Methods: Fundamentals in Single Domains, 563, Scientific Computation, Springer Verlag, New York, 2006.
   Google Scholar
• C. Canuto, M. Hussaini, A. Quarteroni, and T. Zang, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics, 596, Scientifc Computation, Springer Verlag, New York, 2007.
   Google Scholar
• H. G. Silva, and M. M. Villar, Verificação e Validação de Códigos Computacionais, Proceedings Turbulência., pp. 51–94, ABCM—Associação Brasileira de Engenharia e Ciências Mecânicas, Coleção Cadernos de Turbulência, Rio de Janeiro, 2010.
   Google Scholar
• G. Taylor and A. Green, Mechanism of the Production of Small Eddies from Large Ones, Proc. Roy. Soc. Lond. Ser. A Math. Phys. Sci., vol. 158, pp. 499–521, 1937.
   Google Scholar
• A. K. Tornberg and B. Engquist, Numerical Approximations of Singular Source Terms in Differential Equations, J. Comput. Phys., vol. 200, pp. 462–488, 2004.
   Web of Science ®Google Scholar
• F. Mariano, L. Moreira, and A. Silveira-Neto, Mathematical Modeling of Non-periodic Flows Using Fourier Pseudospectral and Immersed Boundary Methods, ECCOMAS-CFD2010—Fifth European Conference on Computational Fluid Dynamics, Proceedings of Fifth European Conference on Computational Fluid Dynamics, 2010.
   Google Scholar
• V. Allampalli, R. Hixon, M. Nallasamy, and S. D. Sawyer, High-Accuracy Large-Step Explicit Runge-Kutta (HALE-RK) Schemes for Computational Aeroacoustics, J. Comput. Phys., vol. 228, pp. 3837–3850, 2009.
   Web of Science ®Google Scholar
• J. W. Cooley and J. W. Tukey, An Algorithm for the Machine Calculation of Complex Fourier Series, Math. Comput., vol. 19, pp. 297–301, 1965.
   Web of Science ®Google Scholar
• R. Courant, K. Friedrichs, and H. Lewy, On the Partial Difference Equations of Mathematical Physic, IBM J. Res. Dev., vol. 11, pp. 215–234, 1965.
   Web of Science ®Google Scholar
• W. D. Henshaw, A Fourth-Order Accurate Method for the Incompressible Navier-Stokes Equations on Overlapping Grids, J. Comput. Phys., vol. 113, pp. 13–25, 1994.
   Web of Science ®Google Scholar
• W. Leong, K. Hollands, and A. Brunger, On a Physically-Realizable Benchmark Problem in Internal Natural Convection, Int. J. Heat Mass Transfer, vol. 41, pp. 3817–3828, 1998.
   Web of Science ®Google Scholar
• D. Wan, B. Patnaik, and G. Wei, A New Benchmark Quality Solution for the Buoyancy-Driven Cavity by Discrete Singular Convolution, Numer. Heat Transfer B, vol. 40, pp. 199–228, 2001.
   Web of Science ®Google Scholar
• P. L. Quéré, Accurate Solutions to the Square Thermally Driven Cavity at High Rayleigh Number, Computers Fluids, vol. 20, pp. 29–41, 1991.
   Web of Science ®Google Scholar
• G. Raithby and H. Wong, Heat Transfer by Natural Convection across Vertical Air Layers, Numer. Heat Transfer, vol. 4, pp. 447–457, 1981.
   Google Scholar
• E. Padilla, R. Campregher, and A. Silveira-Neto, Numerical Analysis of the Natural Convection in Horizontal Annuli at Low and Moderate Ra, Engenharia Térmica (Thermal Engineering), vol. 5, pp. 58–65, 2006.
   Google Scholar
• T. Kuehn and R. Goldstein, An Experimental and Theoretical Study of Natural Convection in the Annulus between Horizontal Concentric Cylinders, J. Fluid Mech., vol. 74, pp. 695–719, 1976.
   Web of Science ®Google Scholar
• J. S. Yoo, Dual Steady Solutions in Natural Convection between Horizontal Concentric Cylinders, Int. J. Heat Fluid Flow, vol. 17, pp. 587–593, 1996.
   Web of Science ®Google Scholar
• D. Takahashi, A Hybrid MPI/OpenMP Implementation of a Parallel 3-D FFT on SMP Clusters, Parallel Process. Appl. Math., vol. 3911, pp. 970–977, 2006.
   Web of Science ®Google Scholar