DEVELOPMENT OF A UNIFIED IMMERSED BOUNDARY-LATTICE BOLTZMANN FLUX SOLVER (UIB-LBFS) FOR SIMULATING FLOWS PAST POROUS OBJECTS

The present work proposed a novel unified immersed boundary-lattice Boltzmann flux solver (UIB-LBFS) for simulating incompressible, 2D/3D, and isothermal/thermal flows past stationary/moving porous objects. The contribution of the present work can be illustrated from the following aspects. First, the developed method unifies the split porous domain and pure fluid domain as one by a diffuse layer, which removes the trouble in conventional methods to identify the point location. Second, the interface boundary conditions are implemented by IBM in a simple way, which also allows flexible computations for different geometries on the same mesh. Next, the employment of LBFS to solve the unified governing equations on the uniform and non-uniform meshes avoids the requirement of the conventional body-fitted mesh. Furthermore, with the help of overset grid technique, the proposed UIB-LBFS can perform successful simulations on moving-boundary problems with complex motions, which can be rather troublesome for conventional methods.

[1] P. Nithiarasu, K. N. Seetharamu, and T. Sundararajan, "Natural convective heat transfer in a fluid saturated variable porosity medium," International Journal of Heat and Mass Transfer, vol. 40, no. 16, pp. 3955-3967, 1997.
[2] A. Bhattacharyya and G. P. Raja Sekhar, "Viscous flow past a porous sphere with an impermeable core : effect of stress jump condition," Chemical Engineering Science, vol. 59, no. 21, pp. 4481-4492, 2004.
[3] T.-C. Jue, "Numerical analysis of vortex behind a porous square cylinder," International Journal of Numerical Methods for Heat & Fluid Flow, vol. 14, pp. 649-663, 2004.
[4] A. R. Martin, C. Saltiel, J. Chai, and W. Shyy, "Convective and radiative internal heat transfer augmentation with fiber arrays," International Journal of Heat and Mass Transfer, vol. 41, pp. 3431-3440, 1998.
[5] D. Couton, S. Doan-Kim, and F. Vuillot, "Numerical simulation of vortex-shedding phenomenon in a channel with flow induced through porous wall," International Journal of Heat and Fluid Flow, vol. 18, pp. 283-296, 1997.
[6] J. S. Chung, M. Olagnon, and C. H. Kim, "The effectiveness of porous damping devices," Proceedings of the 10th (2000) international offshore and polar engineering conference, Vol. III, pp. 418-425, 2000.
[7] P. Yu, "Numerical simulation on oxygen transfer in a porous scaffold for animal cell culture," International Journal of Heat and Mass Transfer, vol. 55, no. 15-16, pp. 4043-4052, 2012.
[8] P. Yu, T. S. Lee, Y. Zeng, and H. T. Low, "Fluid dynamics and oxygen transport in a micro-bioreactor with a tissue engineering scaffold," International Journal of Heat and Mass Transfer, vol. 52, no. 1-2, pp. 316-327, 2009.
[9] D. A. Nield and A. Bejan, Convection in porous media, 5 ed. 2017.
[10] S. Whitaker, "The transport equations for multi-phase systems," Chemical Engineering Science, vol. 28, pp. 139-147, 1973.
[11] W. G. Gray, "A derivation of the equations for multi-phase transport," Chemical engineering science, vol. 30, pp. 229-233, 1975.
[12] S. Whitaker, "Diffusion and dispersion in porous media," AlChE Journal, vol. 13, no. 3, pp. 420-427, 1967.
[13] J. Ni and C. Beckermann, "A volume-averaged two-phase model for transport phenomena during solidification," Metallurgical transactions B, vol. 22, pp. 349-361, 1991.
[14] S. Whitaker, "On the functional dependence of the dispersion vector for scalar transport in porous media," Chemical Engineering Science,, vol. 26, pp. 1893-1899, 1971.
[15] J. C. Slattery, "Flow of viscoelastic fluids through porous media," AlChE Journal, vol. 13, pp. 1066-1071, 1967.
[16] S. Liu, A. Afacan, and J. Masliyah, "Steady incompressible laminar flow in porous media," Chmdml Engineering Science, vol. 49, pp. 3565-3586, 1994.218
[17] O. Rahli, L. Tadrist, M. Miscevic, and R. Santini, "Fluid flow through randomly packed monodisperse fibers: The Kozeny-Carman parameter analysis," Journal of Fluids Engineering, vol. 119, pp. 188-192, 1997.
[18] S. Mauran, L. Rigaud, and O. Coudevylle, "Application of the Carman–Kozeny correlation to a high-porosity and anisotropic consolidated medium: the compressed expanded natural graphite," Transport in Porous Media, vol. 43, pp. 355-376, 2001.
[19] Y. Li and C.-W. Park, "Permeability of packed beds filled with polydisperse spherical particles," Industrial & Engineering Chemistry Research, vol. 37, pp. 2005-2011, 1998.
[20] L. Wang, L.-P. Wang, Z. Guo, and J. Mi, "Volume-averaged macroscopic equation for fluid flow in moving porous media," International Journal of Heat and Mass Transfer, vol. 82, pp. 357-368, 2015.
[21] H. P. G. Darcy, Les Fontaines Publiques de la Ville de Dijon. Paris: Victor Dalmont, 1856.
[22] Lage, The fundamental theory of flow through permeable media: From Darcy to turbulence (Transport Phenomena in Porous Media). Elsevier, Oxford, 1998.
[23] A. S. Altevogt, D. E. Rolston, and S. Whitaker, "New equations for binary gas transport in porous media, Part 2: experimental validation," Advances in Water Resources, vol. 26, no. 7, pp. 717-723, 2003.
[24] A. S. Altevogt, D. E. Rolston, and S. Whitaker, "New equations for binary gas transport in porous media," Advances in Water Resources, vol. 26, no. 7, pp. 695-715, 2003.
[25] J. A. Ochoa-Tapia, F. J. Valdes-Parada, and J. Alvarez-Ramirez, "A fractional-order Darcy's law," Physica A: Statistical Mechanics and its Applications, vol. 374, no. 1, pp. 1-14, 2007.
[26] H. C. Brinkman, "A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles," Appl. Sci. Res. A, vol. 1, pp. 27-34, 1974.
[27] H. C. Brinkman, "On the permeability of media consisting of closely packed porous particles," Appl. Sci. Res. A, vol. 1, pp. 81-86, 1974.
[28] R. A. Wooding, "Steady state free thermal convection of liquid in a saturated permeable medium," Journal of Fluid Mechanics, vol. 2, no. 3, pp. 273-285, 2006.
[29] J. L. Beck, "Convection in a Box of Porous Material Saturated with Fluid," Physics of Fluids, vol. 15, no. 8, 1972.
[30] D. D. Joseph, D. A. Nield, and G. Papanicolaou, "Nonlinear equation governing flow in a saturated porous medium," Water Resources, vol. 18, pp. 1049-1105, 1982.
[31] A. J. E. J. Dupuit, E ́tudes The ́oriques et Pratiques sur le Mouvement des aux dans les Canaux De ́couverts et a Travers les Terrains Perme ́ables. Paris: Victor Dalmont, 1863.
[32] P. Forchheimer, "Wasserbewegung durch Boden," Zeitschrift des Vereines Deutscher Ingenieure, vol. 45, pp. 1736-1741, 1901.
[33] H. C. Brinkman, " A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles," Applied Scientific Research, vol. 1, pp. 27-34, 1947.219
[34] H. C. Brinkman, "On the permeability of media consisting of closely packed porous particles," Applied Scientific Research, vol. A1, pp. 81-86, 1947.
[35] T. S. Lundgren, "Slow flow through stationary random beds and suspensions of spheres," Journal of Fluid Mechanics, vol. 51, no. 2, pp. 273-299, 2006.
[36] N. Martys, D. P. Bentz, and E. J. Garboczi, "Computer simulation study of the effective viscosity in Brinkman’s equation," Physics of Fluids, vol. 6, no. 4, pp. 1434-1439, 1994.
[37] J. Koplik, H. Levine, and A. Zee, "Viscosity renormalization in the Brinkman equation," Physics of Fluids, vol. 26, no. 10, 1983.
[38] S. Liu and J. H. Masliyah, Dispersion in porous media, 2nd ed. ed. (Handbook of Porous Media). Boca Raton, FL: Taylor and Francis, 2005.
[39] J. A. Ochoa-tapia and S. Whitaker, "Momentum transfer at the boundary between a porous; medium and a homogeneous fluid-II.Comparison with experiment," Int. J. Heat Mass Transfer, vol. 38, pp. 2647-2655, 1995.
[40] A. E. Saez, J. C. Perfetti, and I. Rusinek, "Prediction of effective diffusivities in porous media using spatially periodic models," Transport in Porous Media, vol. 6, pp. 143-157, 1991.
[41] R. C. Givler and S. A. Altobelli, "A determination of the effective viscosity for the Brinkman–Forchheimer flow model," Journal of Fluid Mechanics, vol. 258, pp. 355-370, 2006.
[42] C. K. W. Tam, "The drag on a cloud of spherical particles in low Reynolds number flow," Journal of Fluid Mechanics, vol. 38, no. 3, pp. 537-546, 2006.
[43] T. Levy, "Darcy law or Brinkman law?," Comptes rendus de l academie des sciences serie II, vol. 292, pp. 872-874, 1981.
[44] Lage, "Natural convection within a porous medium cavity: Predicting tools for flow regime and heat transfer," International Communications Heat Mass and Transfer, vol. 20, pp. 501-513, 1993.
[45] C. T. Hsu and P. Cheng, "Thermal dispersion in porous medium," International journal of heat and mass transfer, vol. 33, pp. 1587-1597, 1990.
[46] G. S. Beavers and D. D. Joseph, "Boundary conditions at a natural permeable wall," Journal of Fluid Mechanics, vol. 30, pp. 197-207, 1967.
[47] G. S. Beavers, E. M. Sparrow, and R. A. Magnuson, "Experiments on coupled parallel flows in a channel and a bounding porous medium," Journal of Basic Engineering, vol. 92, pp. 843-848, 1970.
[48] G. S. Beavers, E. M. Sparrow, and B. A. Masha, "Boundary condition at a porous surface which bounds a fluid flow," AlChE Journal, vol. 20, pp. 596-597, 1974.
[49] P. Saffman, "On the boundary condition at the surface of a porous meddium," Studies in Applied Mathematics, vol. 50, pp. 93-101, 1971.
[50] I. P. Jones, "Low Reynolds number flow past a porous spherical shell," Mathematical Proceedings of the Cambridge Philosophical Society, vol. 73, no. 1, pp. 231-238, 1973.
[51] B. Straughan, The energy method, stability, and nonlinear convection, 2nd ed. ed. New York: Springer, 2004.220
[52] G. I. Taylor, "A model for the boundary condition of a porous material, Part I," Journal of Fluid Mechanics, vol. 49, p. 319326, 1971.
[53] G. Neale and W. Nader, "Practical significance of Brinkman's extension of Darcy's law: coupled parallel flows within a channel and a bounding porous medium," the Canadian Journal of Chemical Engineering, vol. 52, pp. 475-478, 1974.
[54] J. A. Ochoa-tapia and S. Whitakeri, "Momentum transfer at the boundary between a porous medium and a homogeneous fluid - I.Theoretical development," Int. J. Heat Mass Transfer, vol. 38, pp. 2635-2646, 1995.
[55] J. A. Ochoa-Tapia and S. Whitaker, "Momentum jump condition at the boundary between a prous medium and a homogeneous fluid: Inertial effects," Journal of Porous Media, vol. 1, no. 3, pp. 201-217, 1998.
[56] C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral methods in fluid mechanics. Berlin: Springer, 1987.
[57] M. Fuchs, J. r. Kastner, M. Wagner, S. Hawes, and J. S. Ebersole, "A standardized boundary element method volume conductor model," Clinical Neurophysiology, vol. 113, pp. 702-712, 2002.
[58] A. J. Basu and A. Khalili, "Computation of flow through a fluid-sediment interface in a benthic chamber," Physics of Fluids, vol. 11, no. 6, pp. 1395-1405, 1999.
[59] A. C. Baytas, "Entropy generation for natural convection in an inclined porous cavity," International Journal of Heat and Mass Transfer, vol. 43, pp. 2089-2099, 2000.
[60] Y. Varol, H. F. Oztop, and I. Pop, "Numerical analysis of natural convection in an inclined trapezoidal enclosure filled with a porous medium," International Journal of Thermal Sciences, vol. 47, no. 10, pp. 1316-1331, 2008.
[61] Y. Varol, H. F. Oztop, and I. Pop, "Maximum density effects on buoyancy-driven convection in a porous trapezoidal cavity," International Communications in Heat and Mass Transfer, vol. 37, no. 4, pp. 401-409, 2010.
[62] J. H. Ferziger and M. Peric, Computational methods for fluid dynamics, 3 ed. Berlin: Springer, 2002.
[63] L. Betchen, A. Straatman, and B. Thompson, "A Nonequilibrium Finite-Volume Model for Conjugate Fluid/Porous/Solid Domains," Numerical Heat Transfer: Part A: Applications, vol. 49, no. 6, pp. 543-565, 2006.
[64] S. Bhattacharyya, S. Dhinakaran, and A. Khalili, "Fluid motion around and through a porous cylinder," Chemical Engineering Science, vol. 61, no. 13, pp. 4451-4461, 2006.
[65] S. Akbal and F. Baytaş, "Effects of non-uniform porosity on double diffusive natural convection in a porous cavity with partially permeable wall," International Journal of Thermal Sciences, vol. 47, no. 7, pp. 875-885, 2008.
[66] P. Yu, T. S. Lee, Y. Zeng, and H. T. Low, "A numerical method for flows in porous and homogenous fluid domains coupled at the interface by stress jump," International Journal for Numerical Methods in Fluids, vol. 53, no. 11, pp. 1755-1775, 2007.221
[67] X. Chen, P. Yu, S. H. Winoto, and H. T. Low, "Numerical analysis for the flow past a porous square cylinder based on the stress‐jump interfacial‐conditions," International Journal of Numerical Methods for Heat & Fluid Flow, vol. 18, no. 5, pp. 635-655, 2008.
[68] X. B. Chen, P. Yu, S. H. Winoto, and H. T. Low, "Numerical analysis for the flow past a porous trapezoidal‐cylinder based on the stress‐jump interfacial‐conditions," International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19, no. 2, pp. 223-241, 2009.
[69] P. Yu, Y. Zeng, T. S. Lee, H. X. Bai, and H. T. Low, "Wake structure for flow past and through a porous square cylinder," International Journal of Heat and Fluid Flow, vol. 31, no. 2, pp. 141-153, 2010.
[70] P. Yu, Y. Zeng, T. S. Lee, X. B. Chen, and H. T. Low, "Steady flow around and through a permeable circular cylinder," Computers & Fluids, vol. 42, no. 1, pp. 1-12, 2011.
[71] P. Yu, Y. Zeng, T. S. Lee, X. B. Chen, and H. T. Low, "Numerical simulation on steady flow around and through a porous sphere," International Journal of Heat and Fluid Flow, vol. 36, pp. 142-152, 2012.
[72] M. Bovand, S. Rashidi, M. Dehesht, and J. Abolfazli Esfahani, "Effect of fluid-porous interface conditions on steady flow around and through a porous circular cylinder," International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25, no. 7, pp. 1658-1681, 2015.
[73] M. S. Valipour, S. Rashidi, M. Bovand, and R. Masoodi, "Numerical modeling of flow around and through a porous cylinder with diamond cross section," European Journal of Mechanics - B/Fluids, vol. 46, pp. 74-81, 2014.
[74] K. Anirudh and S. Dhinakaran, "On the onset of vortex shedding past a two-dimensional porous square cylinder," Journal of Wind Engineering and Industrial Aerodynamics, vol. 179, pp. 200-214, 2018.
[75] V. A. F. Costa, L. A. Oliveira, B. R. Baliga, and A. C. M. Sousa, "Simulation of coupled flows in adjacent porous and open domains using a control-volume finite-element method," Numerical Heat Transfer, Part A: Applications, vol. 45, no. 7, pp. 675-697, 2004.
[76] V. A. F. Costa, L. A. Oliveira, and B. R. Baliga, "Implementation of the Stress Jump Condition in a Control-Volume Finite-Element Method for the Simulation of Laminar Coupled Flows in Adjacent Open and Porous Domains," Numerical Heat Transfer, Part B: Fundamentals, vol. 53, no. 5, pp. 383-411, 2008.
[77] T. Basak, S. Roy, T. Paul, and I. Pop, "Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions," International Journal of Heat and Mass Transfer, vol. 49, no. 7-8, pp. 1430-1441, 2006.
[78] T. Duman and U. Shavit, "An Apparent Interface Location as a Tool to Solve the Porous Interface Flow Problem," Transport in Porous Media, vol. 78, no. 3, pp. 509-524, 2008.
[79] J. E. Santos and D. Sheen, "Derivation of a Darcy’s Law for a Porous Medium Composed of Two Solid Phases Saturated by a Single- Phase Fluid: A Homogenization Approach," Transport in Porous Media, vol. 74, no. 3, pp. 349-368, 2008.222
[80] H. Tan and K. M. Pillai, "Finite element implementation of stress-jump and stress-continuity conditions at porous-medium, clear-fluid interface," Computers & Fluids, vol. 38, no. 6, pp. 1118-1131, 2009.
[81] S. Wolfram, "Celluar automation fluids 1: Basic theoryp[J]," J. Stat. Phys., vol. 45, pp. 471-529, 1986.
[82] J. Hardy, Y. Pomeau, and O. de Pazzis, "Time evolution of a two-diemnsional classical lattice systems," Physical Review Letters, vol. 31, pp. 276-279, 1973.
[83] J. Hardy, Y. Pomeau, and O. De Pazzis, "Time evolution of a two-dimensional model ststem I: Invarient states and time correlation functions," J. Math. Phys. , vol. 14, pp. 1746-1759, 1973.
[84] U. Frisch, B. Hasslacher, and Y. Pomeau, "Lattice-gas automata for the Navier-Stokes equations," Phys. Rev. Lett., vol. 56, pp. 1505-1508, 1986.
[85] G. R. McNamara and G. Zanetti, "Use of the Boltzmann Equation to Simulate Lattice-Gas Automata," Physical Review Letters, vol. 61, no. 20, pp. 2332-2335, 1988.
[86] F. Higuera and J. Jimenez, "Boltzmann approach to lattice gas simulations," Europhys. Lett., vol. 9, pp. 663-668, 1989.
[87] F. Higuera, S. Succi, and R. Benzi, "Lattice gas dynamics with enhanced collisions," Europhys. Lett., vol. 9, pp. 345-349, 1989.
[88] S. Chen, H. Chen, D. Martnez, and W. Matthaeus, "Lattice Boltzmann model for simulation of magnetohydrodynamics," Phys Rev Lett, vol. 67, no. 27, pp. 3776-3779, Dec 30 1991.
[89] J. Koelma, "A simple lattice Boltzmann scheme for Navier-Stokes fluid flow," Europhysics Letters, vol. 15, pp. 603-607, 1991.
[90] Y. H. Qian, D. d'Humieres, and P. Lallemand, "Lattice BGK Models for Navier-Stokes Equation," Europhysics letters, vol. 17, no. 6, pp. 479-484, 1992.
[91] S. Chen and G. D. Doolen, "Lattice boltzmann method for fluid flows," Annu. Rev. Fluid Mech., vol. 30, pp. 329-364, 1998.
[92] A. J. C. Ladd, "Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation," Journal of Fluid Mechanics, vol. 271, pp. 285-309, 1994.
[93] A. J. C. Ladd, "Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results," Journal of Fluid Mechanics, vol. 271, pp. 311-339, 1994.
[94] L.-S. Luo, The lattice-gas and lattice Boltzmann methods: Pst, Present, and Future[C]. Beijing, China: The 4th Int, Conf. Appl. Compute. Fluid Dyna, 2000.
[95] F. J. Alexander, S. Chen, and J. D. Sterling, "Lattice Boltzmann thermohydrodynamics," Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, vol. 47, no. 4, pp. R2249-R2252, Apr 1993.
[96] Y. H. Qian, "Simulating thermohydrodynamics with lattice bgk models," Journal of Scientific Computing, vol. 8, no. 3, pp. 231-242, 1993.
[97] Y. Chen, H. Ohashi, and M. Akiyama, "Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations," Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, vol. 50, no. 4, pp. 2776-2783, Oct 1994.223
[98] A. Bartoloni et al., "Lbe simulations of rayleigh-benard convection on the ape100 parallel processor," International Journal of Modern Physics C, vol. 4, no. 5, pp. 993-1006, 1993.
[99] X. Shan, "Simulation of Rayleigh-Be´nard convection using a lattice Boltzmann method," vol. 55, pp. 2780-2788, 1997.
[100] X. He and L.-S. Luo, "Lattice boltzmann model for the incompressible navier-stokes equation," Journal of statistical physics, vol. 88, pp. 927-944, 1997.
[101] B. J. Palmer and D. R. Rector, "Lattice Boltzmann Algorithm for Simulating Thermal Flow in Compressible Fluids," Journal of Computational Physics, vol. 161, no. 1, pp. 1-20, 2000.
[102] Q. Zou, S. Hou, S. Chen, and G. D. Doolen, "An improved incompressible lattice Boltzmann model for time-independent flows," Journal of Statistical Physics, vol. 81, pp. 35-48, 1995.
[103] Y. Wang, C. Shu, and L. M. Yang, "Boundary condition-enforced immersed boundary-lattice Boltzmann flux solver for thermal flows with Neumann boundary conditions," Journal of Computational Physics, vol. 306, pp. 237-252, 2016.
[104] Y. Peng, C. Shu, and Y. T. Chew, "Simplified thermal lattice Boltzmann model for incompressible thermal flows," Phys Rev E Stat Nonlin Soft Matter Phys, vol. 68, no. 2 Pt 2, p. 026701, Aug 2003.
[105] A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti, "Lattice Boltzmann model of immiscible fluids," Phys Rev A, vol. 43, no. 8, pp. 4320-4327, Apr 15 1991.
[106] F. J. Alexander, S. Chen, and D. W. Grunau, "Hydrodynamic spinodal decomposition: Growth kinetics and scaling functions," Phys Rev B Condens Matter, vol. 48, no. 1, pp. 634-637, Jul 1 1993.
[107] D. Grunau, S. Chen, and K. Eggert, "A lattice Boltzmann model for multiphase fluid flows," Physics of Fluids A: Fluid Dynamics, vol. 5, no. 10, pp. 2557-2562, 1993.
[108] X. Shan and H. Chen, "Lattice Boltzmann model for simulating flows with multiple phases and components," Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, vol. 47, no. 3, pp. 1815-1819, Mar 1993.
[109] X. Shan and H. Chen, "Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation," Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, vol. 49, no. 4, pp. 2941-2948, Apr 1994.
[110] M. R. Swift, W. R. Osborn, and J. M. Yeomans, "Lattice Boltzmann simulation of nonideal fluids," Phys Rev Lett, vol. 75, no. 5, pp. 830-833, Jul 31 1995.
[111] A. N. Kalarakis, V. N. Burganos, and A. C. Payatakes, "Galilean-invariant lattice-Boltzmann simulation of liquid-vapor interface dynamics," Physical Review E, vol. 65, no. 5, 2002.
[112] Z.-L. Guo and C. Shu, Lattice Boltzmann method and its applications in engineering. Singapore: World scientific, 2013.
[113] D. H. Rothman, "Cellular-automaton fluids: A model for flow in porous media," Geophysics vol. 53, pp. 509-518, 1988.
[114] S. Succi, E. Foti, and F. Higuera, "Three-dimensional flows in complex geometries with the lattice Boltzmann method," Europhysics letters, vol. 10, pp. 433-438, 1989.224
[115] A. W. Heijs and C. P. Lowe, "Numerical evaluation of the permeability and the Kozeny constant for two types of porous media," Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, vol. 51, no. 5, pp. 4346-4352, May 1995.
[116] C. Pan, M. Hilpert, and C. T. Miller, "Pore-scale modeling of saturated permeabilities in random sphere packings," Phys Rev E Stat Nonlin Soft Matter Phys, vol. 64, no. 6 Pt 2, p. 066702, Dec 2001.
[117] A. K. Gunstensen and D. H. Rothman, "Lattice-Boltzmann studies of immiscible two-phase flow through porous media," Journal of Geophysical Research: Solid Earth, vol. 98, no. B4, pp. 6431-6441, 1993.
[118] R. A. Guyer and K. R. McCall, "Lattice Boltzmann description of magnetization in porous media," Physical Review B, vol. 62, pp. 3674-3688, 2000.
[119] O. Dardis and J. McCloskey, "Lattice Boltzmann scheme with real numbered solid density for the simulation of flow in porous media," Physical Review E, vol. 57, pp. 4834-4837, 1998.
[120] M. A. A. Spaid and F. R. Phelan, "Lattice Boltzmann methods for modeling microscale flow in fibrous porous media," Physics of Fluids, vol. 9, no. 9, pp. 2468-2474, 1997.
[121] Z. Guo and T. S. Zhao, "Lattice Boltzmann model for incompressible flows through porous media," Phys Rev E Stat Nonlin Soft Matter Phys, vol. 66, no. 3 Pt 2B, p. 036304, Sep 2002.
[122] Z. Guo and T. S. Zhao, "A lattice boltzmann model for convection heat transfer in porous media," Numerical heat transfer, Part B, vol. 47, pp. 157-177, 2005.
[123] T. Seta, E. Takegoshi, and K. Okui, "Lattice Boltzmann simulation of natural convection in porous media," Mathematics and Computers in Simulation, vol. 72, no. 2-6, pp. 195-200, 2006.
[124] H. Bai, P. Yu, S. H. Winoto, and H. T. Low, "Lattice Boltzmann method for flows in porous and homogenous fluid domains coupled at the interface by stress jump," International Journal for Numerical Methods in Fluids, vol. 60, no. 6, pp. 691-708, 2009.
[125] V. Babu and A. Narasimhan, "Investigation of vortex shedding behind a porous square cylinder using lattice Boltzmann method," Physics of Fluids, vol. 22, no. 5, 2010.
[126] F. M. Rong, Z. L. Guo, J. H. Lu, and B. C. Shi, "Numerical simulation of the flow around a porous covering square cylinder in a channel via lattice Boltzmann method," International Journal for Numerical Methods in Fluids, vol. 65, no. 10, pp. 1217-1230, 2011.
[127] Y. Zhang, N. Ozalp, and G. Xie, "LBM modelling unsteady flow past and through permeable diamond-shaped cylinders," International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29, no. 9, pp. 3472-3497, 2019.
[128] M. Pepona and J. Favier, "A coupled Immersed Boundary–Lattice Boltzmann method for incompressible flows through moving porous media," Journal of Computational Physics, vol. 321, pp. 1170-1184, 2016.225
[129] K. Vafai and S. J. Kim, "Fluid mechanics of the interface region between a porous medium and a fluid layer –an exact solution," International Journal of Heat and Fluid Flow, vol. 11, pp. 254-256, 1990.
[130] M. R. H. Nobari and H. Naderan, "A numerical study of flow past a cylinder with cross flow and inline oscillation," Computers & Fluids, vol. 35, no. 4, pp. 393-415, 2006.
[131] S. Bhattacharyya and A. K. Singh, "Augmentation of heat transfer from a solid cylinder wrapped with a porous layer," International Journal of Heat and Mass Transfer, vol. 52, no. 7-8, pp. 1991-2001, 2009.
[132] S. Dhinakaran and J. Ponmozhi, "Heat transfer from a permeable square cylinder to a flowing fluid," Energy Conversion and Management, vol. 52, no. 5, pp. 2170-2182, 2011.
[133] S. Rashidi, A. Tamayol, M. S. Valipour, and N. Shokri, "Fluid flow and forced convection heat transfer around a solid cylinder wrapped with a porous ring," International Journal of Heat and Mass Transfer, vol. 63, pp. 91-100, 2013.
[134] K. Anirudh and S. Dhinakaran, "Effects of Prandtl number on the forced convection heat transfer from a porous square cylinder," International Journal of Heat and Mass Transfer, vol. 126, pp. 1358-1375, 2018.
[135] C. Shu, Y. Wang, C. J. Teo, and J. Wu, "Development of Lattice Boltzmann Flux Solver for Simulation of Incompressible Flows," Advances in Applied Mathematics and Mechanics, vol. 6, no. 4, pp. 436-460, 2014.
[136] C. S. Peskin, "Numerical analysis of blood flow in the heart," Journal of Computational Physics, vol. 25, pp. 220-252, 1977.
[137] M.-C. Lai and C. S. Peskin, "An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity," Journal of Computational Physics, vol. 160, no. 2, pp. 705-719, 2000.
[138] Y. Wang, C. Shu, C. J. Teo, and J. Wu, "An immersed boundary-lattice boltzmann flux solver and its applications to fluid–structure interaction problems," Journal of Fluids and Structures, vol. 54, pp. 440–465, 2015.
[139] Y. Wang, C. Shu, C. J. Teo, and L. M. Yang, "An efficient immersed boundary-lattice Boltzmann flux solver for simulation of 3D incompressible flows with complex geometry," Computers & Fluids, vol. 124, pp. 54-66, 2016.
[140] Y. Wang, C. Shu, and C. J. Teo, "Thermal lattice Boltzmann flux solver and its application for simulation of incompressible thermal flows," Computers & Fluids, vol. 94, pp. 98-111, 2014.
[141] R. Mittal and G. Iaccarino, "Immersed Boundary Methods," Annual Review of Fluid Mechanics, vol. 37, no. 1, pp. 239-261, 2005.
[142] Y.-H. Tseng and J. H. Ferziger, "A ghost-cell immersed boundary method for flow in complex geometry," Journal of Computational Physics, vol. 192, no. 2, pp. 593-623, 2003.
[143] Z.-G. Feng and E. E. Michaelides, "The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems," Journal of Computational Physics, vol. 195, no. 2, pp. 602-628, 2004.
[144] Z.-G. Feng and E. E. Michaelides, "Proteus: a direct forcing method in the simulations of particulate flows," Journal of Computational Physics, vol. 202, no. 1, pp. 20-51, 2005.226
[145] M. Uhlmann, "An immersed boundary method with direct forcing for the simulation of particulate flows," Journal of Computational Physics, vol. 209, no. 2, pp. 448-476, 2005.
[146] X. D. Niu, C. Shu, Y. T. Chew, and Y. Peng, "A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows," Physics Letters A, vol. 354, no. 3, pp. 173-182, 2006.
[147] S.-W. Su, M.-C. Lai, and C.-A. Lin, "An immersed boundary technique for simulating complex flows with rigid boundary," Comput Fluids, vol. 36, pp. 313-324, 2007.
[148] C. Shu, N. Liu, and Y. T. Chew, "A novel immersed boundary velocity correction–lattice Boltzmann method and its application to simulate flow past a circular cylinder," Journal of Computational Physics, vol. 226, no. 2, pp. 1607-1622, 2007.
[149] J. Wu and C. Shu, "Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications," Journal of Computational Physics, vol. 228, no. 6, pp. 1963-1979, 2009.
[150] X. Yang, X. Zhang, Z. Li, and G.-W. He, "A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations," Journal of Computational Physics, vol. 228, no. 20, pp. 7821-7836, 2009.
[151] C. Ji, A. Munjiza, and J. J. R. Williams, "A novel iterative direct-forcing immersed boundary method and its finite volume applications," Journal of Computational Physics, vol. 231, no. 4, pp. 1797-1821, 2012.
[152] C. Cheng, S. A. Galindo-Torres, X. Zhang, P. Zhang, A. Scheuermann, and L. Li, "An improved immersed moving boundary for the coupled discrete element lattice Boltzmann method," Computers & Fluids, vol. 177, pp. 12-19, 2018.
[153] A. K. De, "A diffuse interface immersed boundary method for complex moving boundary problems," Journal of Computational Physics, vol. 366, pp. 226-251, 2018.
[154] J. Kim, "A continuous surface tension force formulation for diffuse-interface models," Journal of Computational Physics, vol. 204, no. 2, pp. 784-804, 2005.
[155] H. Ding, P. D. M. Spelt, and C. Shu, "Diffuse interface model for incompressible two-phase flows with large density ratios," Journal of Computational Physics, vol. 226, no. 2, pp. 2078-2095, 2007.
[156] H. Z. Yuan, Z. Chen, C. Shu, Y. Wang, X. D. Niu, and S. Shu, "A free energy-based surface tension force model for simulation of multiphase flows by level-set method," Journal of Computational Physics, vol. 345, pp. 404-426, 2017.
[157] Z. Guo, B. Shi, and C. Zheng, "A coupled lattice BGK model for the Boussinesq equations," International journal for numerical methods in fluids, vol. 39, pp. 325-342, 2002.
[158] K. Suzuki and T. Inamuro, "Effect of internal mass in the simulation of a moving body by the immersed boundary method," Computers & Fluids, vol. 49, no. 1, pp. 173-187, 2011.
[159] P. D. Noymer, L. R. Glicksman, and A. Devendran, "Drag on a permeable cylinder in steady flow at moderate Reynolds numbers," Chemical Engineering Science, vol. 53, pp. 2859-2869, 1998.227
[160] T. Sueki, T. Takaishi, M. Ikeda, and N. Arai, "Application of porous material to reduce aerodynamic sound from bluff bodies," Fluid Dynamics Research, vol. 42, no. 1, 2010.
[161] M. Braza, P. Chassaing, and H. H. Minh, "Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder," Journal of Fluid Mechanics, vol. 165, no. -1, 2006.
[162] H. Ding, C. Shu, K. S. Yeo, and D. Xu, "Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method," Computer Methods in Applied Mechanics and Engineering, vol. 193, no. 9-11, pp. 727-744, 2004.
[163] M. G. Benson, P. G. Bellamy-Knights, and J. H. Gerrard, "A viscous splitting algorithm applied to low reynolds number flows round a circular cylinder," Journal of Fluids and Structures, vol. 3, pp. 439-479, 1989.
[164] H. V. R. Mittal, J. C. Kalita, and R. K. Ray, "A class of finite difference schemes for interface problems with an HOC approach," International Journal for Numerical Methods in Fluids, vol. 82, no. 9, pp. 567-606, 2016.
[165] S. Yu, P. Yu, and T. Tang, "Effect of thermal buoyancy on flow and heat transfer around a permeable circular cylinder with internal heat generation," International Journal of Heat and Mass Transfer, vol. 126, pp. 1143-1163, 2018.
[166] S. Yu, T. Tang, J. Li, and P. Yu, "Wake and thermal characteristics for crossbuoyancy mixed convection around and through a porous cylinder," Physics of Fluids, vol. 32, no. 6, p. 073603, Jun 1 2020.
[167] B. Alazmi and K. Vafai, "Analysis of fuid fow and heat transfer interfacial conditions between a porous medium and a fuid layer," International Journal of Heat and Mass Transfer, vol. 44, pp. 1735-1749, 2001.
[168] Z. Guo, B. Shi, and N. Wang, "Lattice BGK Model for Incompressible Navier–Stokes Equation," Journal of Computational Physics, vol. 165, no. 1, pp. 288-306, 2000.
[169] Y. Wang, L. Yang, and C. Shu, "From Lattice Boltzmann Method to Lattice Boltzmann Flux Solver," Entropy, vol. 17, no. 12, pp. 7713-7735, 2015.
[170] H. Chen, P. Yu, and C. Shu, "A unified immersed boundary-lattice Boltzmann flux solver (UIB-LBFS) for simulation of flows past porous bodies," Physics of Fluids, vol. 33, no. 8, 2021.
[171] W. Ren, C. Shu, and W. Yang, "An efficient immersed boundary method for thermal flow problems with heat flux boundary conditions," International Journal of Heat and Mass Transfer, vol. 64, pp. 694-705, 2013.
[172] S. Tao, A. Xu, Q. He, B. Chen, and F. G. F. Qin, "A curved lattice Boltzmann boundary scheme for thermal convective flows with Neumann boundary condition," International Journal of Heat and Mass Transfer, vol. 150, 2020.
[173] J.-S. Yoo, "Dual free-convective flows in a horizontal annulus with a constant heat flux wall," International Journal of Heat and Mass Transfer, vol. 46, no. 13, pp. 2499-2503, 2003.228
[174] K. Khanafer, A. Al-Amiri, and I. Pop, "Numerical analysis of natural convection heat transfer in a horizontal annulus partially filled with a fluid-saturated porous substrate," International Journal of Heat and Mass Transfer, vol. 51, no. 7-8, pp. 1613-1627, 2008.
[175] T. R. Vijaybabu, K. Anirudh, and S. Dhinakaran, "Mixed convective heat transfer from a permeable square cylinder: A lattice Boltzmann analysis," International Journal of Heat and Mass Transfer, vol. 115, pp. 854-870, 2017.
[176] Z. Chen, C. Shu, and D. Tan, "A simplified thermal lattice Boltzmann method without evolution of distribution functions," International Journal of Heat and Mass Transfer, vol. 105, pp. 741-757, 2017.
[177] A. P. Hatton, D. D. James, and H. W. Swire, "Combined forced and natural convection with low-speed air flow over horizontal cylinders," Journal of Fluid Mechanics, vol. 42, no. 1, pp. 17-31, 2006.
[178] H. M. Badr, "Laminar combined convection from a horizontal cylinder-parallel and contra flow regimes," International Journal of Heat and Mass Transfer, vol. 27, pp. 15-27, 1984.
[179] J. M. Shi, D. Gerlach, M. Breuer, G. Biswas, and F. Durst, "Heating effect on steady and unsteady horizontal laminar flow of air past a circular cylinder," Physics of Fluids, vol. 16, no. 12, pp. 4331-4345, 2004.
[180] Y. Wang, C. Shu, and C. J. Teo, "Development of LBGK and incompressible LBGK-based lattice Boltzmann flux solvers for simulation of incompressible flows," International Journal for Numerical Methods in Fluids, vol. 75, no. 5, pp. 344-364, 2014.
[181] H. Dong and L. M. Yang, "An Immersed Boundary-Simplified Gas Kinetic Scheme for 2D Incompressible Flows with Curved and Moving Boundaries," Advances in Applied Mathematics and Mechanics, vol. 11, no. 5, pp. 1177-1199, 2019.
[182] E. Guilmineau and P. Queutey, "A numerical simulation of vortex shedding from an oscillating circular cylinder," Journal of Fluids and Structures, vol. 16, no. 6, pp. 773-794, 2002.
[183] Z. Chen, C. Shu, and D. Tan, "Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows," Physics of Fluids, vol. 30, no. 5, 2018.
[184] S. Mittal and B. Kumar, "Flow past a rotating cylinder," Journal of Fluid Mechanics, vol. 476, pp. 303-334, 2003.
[185] X. Zhao, Z. Chen, L. Yang, N. Liu, and C. Shu, "Efficient boundary condition-enforced immersed boundary method for incompressible flows with moving boundaries," Journal of Computational Physics, vol. 441, 2021.
[186] Y. Wang, C. Shu, C. J. Teo, J. Wu, and L. Yang, "Three-Dimensional Lattice Boltzmann Flux Solver and Its Applications to Incompressible Isothermal and Thermal Flows," Communications in Computational Physics, vol. 18, no. 3, pp. 593-620, 2015.
[187] H. Ding, C. Shu, K. S. Yeo, and D. Xu, "Numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method," Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 7-8, pp. 516-533, 2006.229
[188] A. Emadzadeh and Y.-M. Chiew, "Settling Velocity of Porous Spherical Particles," Journal of Hydraulic Engineering, vol. 146, no. 1, 2020.
[189] J. Kim, D. Kim, and H. Choi, "An Immersed-Boundary Finite-Volume Method for Simulations of Flow in Complex Geometries," Journal of Computational Physics, vol. 171, no. 1, pp. 132-150, 2001.
[190] A. Gilmanov, F. Sotiropoulos, and E. Balaras, "A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids," Journal of Computational Physics, vol. 191, no. 2, pp. 660-669, 2003.
[191] X. Y. Wang, K. S. Yeo, C. S. Chew, and B. C. Khoo, "A SVD-GFD scheme for computing 3D incompressible viscous fluid flows," Computers & Fluids, vol. 37, no. 6, pp. 733-746, 2008.
[192] J. H. Masliyah and M. Polikar, "Terminal velocity of porous spheres," the Canadian Journal of Chemical Engineering, vol. 58, pp. 299-302, 1980.
[193] A. G. Tomboulides, S. A. Orszag, and G. E. Karniadakis, "Direct and large-eddy simulations of axisymmetric wakes," 31st Aerospace Sciences Meeting & Exhibit, pp. 1-12, 1993.
[194] J. Jeong and F. Hussain, "On the identification of a vortex," vol. 285, pp. 69-94, 1995.
[195] J. Wu and C. Shu, "Simulation of three-dimensional flows over moving objects by an improved immersed boundary-lattice Boltzmann method," International Journal for Numerical Methods in Fluids, vol. 68, no. 8, pp. 977-1004, 2012.