Immersed boundary method for the simulation of heat transfer and fluid flow based on vorticity–velocity formulation

References

• C. Peskin, The Immersed Boundary Method, Acta Numer., vol. 11, pp. 479–517, 2002.
   Google Scholar
• R. Mittal and G. Iaccarino, Immersed Boundary Methods, Annu. Rev. Fluid Mech., vol. 37, pp. 239–261, 2005.
   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, no. 2, pp. 354–366, 1999.
   Web of Science ®Google Scholar
• J. Mohd-Yusof, Combined Immersed Boundary/B-splines Method for Simulations of Flows in Complex Geometry, CTR Annual Research Briefs in NASA Ames Research Center/Stanford University Center for Turbulence Research, pp. 317–327, 1997.
   Google Scholar
• Z. Wang, J. Fan, and K. Luo, Combined Multi-direct Forcing and Immersed Boundary Method for Simulating Flows with Moving Particles, Int. J. Multiphas. Flow, vol. 34, pp. 283–302, 2008.
   Web of Science ®Google Scholar
• M. Uhlmann, An Immersed Boundary Method with Direct Forcing For the Simulation of Particulate Flows, J. Comput. Phys., vol. 209, no. 2, pp. 448–476, 2005.
   Web of Science ®Google Scholar
• C. Canuto, M. Hussaini, A. Quarteroni, and T. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, 1987.
   Google Scholar
• G. Keetels, U. D’Ortona, W. Kramer, H. Clercx, K. Schneider, and G. van Heijst, Fourier Spectral and Wavelet Solvers for the Incompressible Navier–Stokes Equations with Volume-penalization: Convergence of a Dipole-wall Collision, J. Comput. Phys., vol. 227, no. 2, pp. 919–945, 2007.
   Web of Science ®Google Scholar
• D. Kolomenskiy and K. Schneider, A Fourier Spectral Method for the Navier–Stokes Equations with Volume Penalization for Moving Solid Obstacles, J. Comput. Phys., vol. 228, no. 16, pp. 5687–5709, 2009.
   Web of Science ®Google Scholar
• J. Kim and H. Choi, An Immersed-boundary Finite-volume Method for Simulation of Heat Transfer in Complex Geometries, KSME Int. J., vol. 18, pp. 1026–1035, 2004.
   Web of Science ®Google Scholar
• J. Pacheco, A. Pacheco-Vega, T. Rodic, and R. Peck, Numerical Simulation of Heat Transfer and Fluid Flow Problems Using an Immersed-boundary Finite-volume Method on Nonstaggered Grids, Numer. Heat Transfer B Fund., vol. 48, pp. 1–24, 2005.
   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
• C. Liao and C. Lin, Simulations of Natural and Forced Convection Flows with Moving Embedded Object Using Immersed Boundary Method, Comput. Method. Appl. Mech. Eng., vol. 213, pp. 58–70, 2012.
   Web of Science ®Google Scholar
• W. Ren, C. Shu, J. Wu, and W. Yang, Boundary Condition-enforced Immersed Boundary Method for Thermal Flow Problems with Dirichlet Temperature Condition and Its Applications, Comput. Fluids, vol. 57, pp. 40–51, 2012.
   Web of Science ®Google Scholar
• F. Sabetghadam and E. Soltani, Simulation of Solid Body Motion in a Newtonian Fluid Using a Vorticity-based Pseudo-spectral Immersed Boundary Method Augmented by the Radial Basis Functions, Int. J. Mod. Phys. C, vol. 26, p. 1550053, 2015.
   Web of Science ®Google Scholar
• D. Rempfer, On Boundary Conditions for Incompressible Navier–Stokes Problems, Appl. Mech. Rev., vol. 59, no. 3, 2006.
   Web of Science ®Google Scholar
• D. Calhoun, A Cartesian Grid Method for Solving the Two-dimensional Stream Function-vorticity Equations in Irregular Regions, J. Comput. Phys., vol. 176, pp. 231–275, 2002.
   Web of Science ®Google Scholar
• L. Quartapelle, Vorticity Conditioning in the Computation of Two-dimensional Viscous Flows, J. Comput. Phys., vol. 40, pp. 453–477, 1981.
   Web of Science ®Google Scholar
• M. Vanella and E. Balaras, A Moving-least-squares Reconstruction for Embedded-boundary Formulations, J. Comput. Phys., vol. 228, no. 18, pp. 6617–6628, 2009.
   Web of Science ®Google Scholar
• C. De boor and A. Ron, The Least Solution for the Polynomial Interpolation Problem, Math. Z., vol. 210, pp. 347–378, 1992.
   Web of Science ®Google Scholar
• P. Chinchapatnam, K. Djidjeli, and P. Nair, Radial Basis Function Meshless Method for the Steady Incompressible Navier–Stokes Equations, Int. J. Comput. Math., vol. 84, no. 10, pp. 1509–1521, 2007.
   Web of Science ®Google Scholar
• E. Larsson and B. Fornberg, A Numerical Study of Some Radial Basis Function Based Solution Methods for Elliptic PDEs, Comput. Math. Appl., vol. 46, pp. 891–902, 2003.
   Web of Science ®Google Scholar
• N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, Wiley, New York, 1949.
   Google Scholar
• R. Deutsch, Estimation Theory, Prentice-Hall, New Jersey, 1965.
   Google Scholar
• D. Shepard, A Two-dimensional Interpolation Function for Irregularly Spaced Data, Proc. 23rd ACM Nat. Conf., pp. 517–523, 1968.
   Google Scholar
• R. Franke and G. Nielson, Smooth Interpolation of Large Sets of Scattered Data, Int. J. Numer. Meth. Eng., vol. 15, pp. 1691–1704, 1980.
   Web of Science ®Google Scholar
• R. Renka and R. Brown, Algorithm 790: CSHEP2D: Cubic Shepard Method for Bivariate Interpolation of Scattered Data, ACM Trans. Math. Software, vol. 25, 1999.
   Web of Science ®Google Scholar
• W. Shizhao and X. Zhang, An Immersed Boundary Method Based on Discrete Stream Function Formulation for Two- and Three-dimensional Incompressible Flows, J. Comput. Phys., vol. 230, pp. 3479–3499, 2011.
   Web of Science ®Google Scholar
• A. Lee and D. You, An Implicit Ghost-cell Immersed Boundary Method for Simulations of Moving Body Problems with Control of Spurious Force Oscillations, J. Comput. Phys., vol. 233, pp. 295–314, 2013.
   Web of Science ®Google Scholar
• M. Coutanceau and R. Bouard, Experimental Determination of the Main Features of the Viscous Flow in the Wake of a Circular Cylinder in Uniform Translation, J. Fluid Mech., vol. 79, pp. 231–256, 1977.
   Web of Science ®Google Scholar
• R. Bharti, R. Chhabra, and V. Eswaran, A Numerical Study of the Steady Forced Convection Heat Transfer from an Unconfined Circular Cylinder, Heat Mass Transfer, vol. 43, pp. 639–648, 2007.
   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
• E. Eckert and E. Soehngen, Distribution of Heat-transfer Coefficients around Circular Cylinders in Crossflow at Reynolds Numbers from 20 to 500, Trans. ASME, vol. 75, pp. 343–347, 1952.
   Google Scholar
• K. Momose and H. Kimoto, Forced Convection Heat Transfer from a Heated Circular Cylinder with Arbitrary Surface Temperature Distributions, Heat Transfer Asian Res., vol. 28, no. 6, pp. 484–499, 1999.
   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
• M. Sheikholeslami, M. Gorji-Bandpy, I. Pop, and S. Soleimani, Numerical Study of Natural Convection between a Circular Enclosure and a Sinusoidal Cylinder Using Control Volume Based Finite Element Method, Int. J. Therm. Sci., vol. 72, pp. 147–158, 2013.
   Web of Science ®Google Scholar
• M. Linnick and H. Fasel, A High-order Immersed Interface Method for Simulating Unsteady Incompressible Flows on Irregular Domains, J. Comput. Phys., vol. 204, no. 1, pp. 157–192, 2005.
   Web of Science ®Google Scholar
• K. Taira and T. Colonius, The Immersed Boundary Method: A Projection Approach, J. Comput. Phys., vol. 225, no. 2, pp. 2118–2137, 2007.
   Web of Science ®Google Scholar
• Z. Wang, J. Fan, and K. Cen, Immersed Boundary Method for the Simulation of 2D Viscous Flow Based on Vorticity–Velocity Formulations, J. Comput. Phys., vol. 228, no. 5, pp. 1504–1520, 2008.
   Web of Science ®Google Scholar
• Y. Wu, G. Liu, and Y. Gu, Application of Meshless Local Petrov–Galerkin (MLPG) Approach to Simulation of Incompressible Flow, Numer. Heat Transfer B Fund., vol. 48, pp. 459–475, 2005.
   Web of Science ®Google Scholar
• C. Shu, Application of Differential Quadrature Method to Simulate Natural Convection in a Concentric Annulus, Int. J. Numer. Meth. Fl., vol. 30, pp. 977–993, 1999.
   Web of Science ®Google Scholar
• J. Yoo, Mixed Convection of Air between Two Horizontal Concentric Cylinders with a Cooled Rotating Outer Cylinder, Int. J. Heat Mass Transfer, vol. 41, no. 2, pp. 293–302, 1998.
   Web of Science ®Google Scholar