A dynamically adaptive lattice Boltzmann method for thermal convection problems

Abdelhadi, B., Hamza, G., Razik, B. and Raouache, E. (2006). Natural convection and turbulent instability in cavity, WSEAS Transactions on Heat and Mass Transfer 1(2): 179-184.Search in Google Scholar

Alexander, F.J., Chen, S. and Sterling, J.D. (1993). Lattice Boltzmann thermohydrodynamics, Physical Review E 47: 2249-2252.10.1103/PhysRevE.47.R2249Search in Google Scholar

Azwadi Che Sidik, N. and Irwan, M. (2010). Simplified mesoscale lattice Boltzmann numerical model for prediction of natural convection in a square enclosure filled with homogeneous porous media, WSEAS Transactions on Fluid Mechanics 3(5): 186-195.Search in Google Scholar

Azwadi Che Sidik, N. and Syahrullail, S. (2009). A three-dimension double-population thermal lattice BGK model for simulation of natural convection heat transfer in a cubic cavity, WSEAS Transactions on Mathematics 8(9): 561-571.Search in Google Scholar

Berger, M. and Colella, P. (1988). Local adaptive mesh refinement for shock hydrodynamics, Journal of Computational Physics 82(1): 64-84.10.1016/0021-9991(89)90035-1Search in Google Scholar

Bhatnagar, P., Gross, E. and Krook, M. (1954). A model for collisional processes in gases, I: Small amplitude processes in charged and in neutral one-component systems, Physical Review 94(3): 511-525.10.1103/PhysRev.94.511Search in Google Scholar

Bouzidi, M., Firdaouss, M. and Lallemand, P. (2001). Momentum transfer of a Boltzmann-lattice fluid with boundaries, Physics of Fluids 13(11): 3452-3459.10.1063/1.1399290Search in Google Scholar

Chen, H., Filippova, O., Hoch, J., Molvig, K., Shock, R., Teixeira, C. and Zhang, R. (2006). Grid refinement in lattice Boltzmann methods based on volumetric formulation, Physica A 362(1): 158-167.10.1016/j.physa.2005.09.036Search in Google Scholar

Chen, H. and Teixeira, C. (2000). H-theorem and origins of instability in thermal lattice Boltzmann models, Computer Physics Communications 129(1): 21-31.10.1016/S0010-4655(00)00089-8Search in Google Scholar

Chen, S. and Doolen, G. (1998). Lattice Boltzmann method for fluid flows, Annual Review of Fluid Mechanics 30: 329-364.10.1146/annurev.fluid.30.1.329Search in Google Scholar

Coutanceau, M. and Menard, C. (1985). Influence of rotation on the near-wake development behind an impulsively started circular cylinder, Journal of Fluid Mechanics 158: 399-446.10.1017/S0022112085002713Search in Google Scholar

De Vahl Davis, G. (1983). Natural convection of air in a square cavity a benchmark numerical solution, International Journal for Numerical Methods in Fluids 3(3): 249-264.10.1002/fld.1650030305Search in Google Scholar

Deiterding, R. (2011). Block-structured adaptive mesh refinement-theory, implementation and application, ESAIM Proceedings 34: 97-150.10.1051/proc/201134002Search in Google Scholar

Deller, P. (2002). Lattice kinetic schemes for magnetohydrodynamics, Journal of Computational Physics 179(1): 95-126.10.1006/jcph.2002.7044Search in Google Scholar

Dupuis, A. and Chopard, B. (2003). Theory and applications of an alternative lattice Boltzmann grid refinement algorithm, Physica E 67: 066707.10.1103/PhysRevE.67.066707Search in Google Scholar

Fusegi, T., Hyun, J., Kuwahara, K. and Farouk, B. (1991). A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure, International Journal of Heat and Mass Transfer 34(6): 1543-1557.10.1016/0017-9310(91)90295-PSearch in Google Scholar

Guo, Z., Shi, B. and Zheng, C. (2002). A coupled lattice BGK model for the Boussinesq equations, International Journal for Numerical Methods in Fluids 39(4): 325-342.10.1002/fld.337Search in Google Scholar

Hähnel, D. (2004). Molekulare Gasdynamik, Springer, Heidelberg.Search in Google Scholar

He, N.-Z., Wang, N.-C., Shi, B.-C. and Guo, Z.-L. (2004). A unified incompressible lattice BGK model and its application to three-dimensional lid-driven cavity flow, Chinese Physics 13(1): 40-46.10.1088/1009-1963/13/1/009Search in Google Scholar

He, X., Chen, S. and Doolen, G. (1998). A novel thermal model for the lattice Boltzmann method in incompressible limit, Journal of Computational Physics 146(1): 282-300.10.1006/jcph.1998.6057Search in Google Scholar

He, X. and Luo, L.-S. (1997). Lattice Boltzmann model for the incompressible Navier-Stokes equation, Journal of Statistical Physics 88(3): 927-944.10.1023/B:JOSS.0000015179.12689.e4Search in Google Scholar

Jonas, L., Chopard, B., Succi, S. and Toschi, F. (2006). Numerical analysis of the average flow field in a turbulent lattice Boltzmann simulation, Physica A 32(1): 6-10.10.1016/j.physa.2005.09.016Search in Google Scholar

Kuznik, F., Vareilles, J., Rusaouen, G. and Kraiss, G. (2007). A double-population lattice Boltzmann method with non-uniform mesh for the simulation of natural convection in a square cavity, International Journal of Heat and Fluid Flow 28(5): 862-870.10.1016/j.ijheatfluidflow.2006.10.002Search in Google Scholar

Lai, H. and Yan, Y. (2001). The effect of choosing dependent variables and cell-face velocities on convergence of the SIMPLE algorithm using non-orthohonal grids, International Journal of Numerical Methods for Heat & Fluid Flow 11(6): 524-546.10.1108/EUM0000000005667Search in Google Scholar

Lee, T. and Lin, C. (2005). A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, Journal of Computational Physics 206(1): 16-47.10.1016/j.jcp.2004.12.001Search in Google Scholar

Li, L., Mei, R. and Klausner, J. (2013). Boundary conditions for thermal lattice Boltzmann equation method, Journal of Computational Physics 237(1): 366-395.10.1016/j.jcp.2012.11.027Search in Google Scholar

McNamara, G. and Alder, B. (1993). Analysis of lattice Boltzmann treatment of hydrodynamics, Physica A 194(1): 218-228.10.1016/0378-4371(93)90356-9Search in Google Scholar

Mohamad, A. (2011). Lattice Boltzmann Method- Fundamentals and Engineering Applications with Computer Codes, Springer, London.10.1007/978-0-85729-455-5Search in Google Scholar

Mohamad, A. and Kuzmin, A. (2010). A critical evaluation of force term in lattice Boltzmann method, natural convection problem, International Journal of Heat and Mass Transfer 53: 990-996.10.1016/j.ijheatmasstransfer.2009.11.014Search in Google Scholar

Peng, Y., Shu, C. and Che, Y. (2003). A 3D incompressible thermal lattice Boltzman model and its application to simulation natural convection in a cubic cavity, Journal of Computational Physics 193(1): 260-274.10.1016/j.jcp.2003.08.008Search in Google Scholar

Qian, Y. (1993). Simulating thermohydrodynamics with lattice BGK models, Journal of Scientific Computing 8(3): 231-241.10.1007/BF01060932Search in Google Scholar

Qian, Y., D’Humires, D. and Lallemand, P. (1992). Lattice BGK models for Navier-Stokes equation, Europhysics Letters 17(6): 479-484.10.1209/0295-5075/17/6/001Search in Google Scholar

Succi, S. (2001). The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond, Numerical Mathematics and Scientific Computation, Clarendon Press, Oxford.Search in Google Scholar

Yan, Y. and Zu, Y. (2008). Numerical simulation of heat transfer and fluid flow past a rotating isothermal cylinder-A LBM approach, International Journal of Heat and Mass Transfer 51(9-10): 2519-2536.10.1016/j.ijheatmasstransfer.2007.07.053Search in Google Scholar

Yu, Z. and Fan, L.-S. (2009). An interaction potential based lattice Boltzmann method with adaptive mesh refinement (AMR) for two-phase flow simulation, Journal of Computational Physics 230(17): 6456-6478.10.1016/j.jcp.2009.05.034Search in Google Scholar