Lattice Boltzmann Method Applied to Radiative Transport Analysis in a Planar Participating Medium

Analysis of Rayleigh-Bénard convection with thermal volumetric radiation using Lattice Boltzmann Formulation

“…However, as the complexity of the problem increases, with LBM as the solvers for, say the momentum and energy equations, and one of the CFD methods for computation of radiative information, for the reasons stated above, the computational time becomes exorbitant (Mishra et al, 2014a(Mishra et al, , 2014b.…”

“…The usage of the LBM to formulate and solve different types of heat transfer problems involving volumetric radiation in different geometries has been extended (Mishra et al, 2014a, Chen and Zhang, 1999, Succi, 2001, Wang et al, 2013, Jiaung et al, 2001, Lankadasu and Mishra, 2005, Chaabane et al, 2011a, 2011b, Mishra and Mondal, 2009, Chaabane et al, 2011c. However, in all such problems, although the radiative information was computed using the conventional RTE solvers and in terms of formulation and computational time, the solution of the energy equation by the LBM was encouraging.…”

“…In solving this set of governing partial differential and integro-differential equations, periodic boundary conditions have been used for both hydrodynamic and thermal fields for the vertical walls and no-slip isothermal boundary conditions were imposed along the bottom and the top boundaries (Mishra et al, 2014a).…”

“…In the recent past, the lattice Boltzmann method (LBM) has emerged as an efficient method to analyze a vast range of problems in fluid flow and heat transfer (Chen and Zhang, 1999, Succi, 2001, Wang et al, 2013, Jiaung et al, 2001, Lankadasu and Mishra, 2005, Chaabane et al, 2011a, 2011b, Mishra and Mondal, 2009, Chaabane et al, 2011c, Asinari et al, 2010and Di Rienzo et al, 2011. Unlike conventional methods, which solve the discretized macroscopic Navier-Stokes equations, the LBM uses simple microscopic kinetic models to stimulate complex transport phenomena.So, this surge in applications of the LBM, compared to existing CFD solvers, is owing to its simple calculation procedure, mesoscopic nature, simple and efficient implementation for parallel computation, easy, robust straight forward and efficient handing of complex geometry and boundary conditions, high computational performance with regard to stability, accuracy and precision and memory overhead over other methods (Succi, 2001).The usage of the LBM to formulate and solve different types of heat transfer problems involving volumetric radiation in different geometries has been extended (Mishra et al, 2014a, Chen and Zhang, 1999, Succi, 2001, Wang et al, 2013, Jiaung et al, 2001, Lankadasu and Mishra, 2005, Chaabane et al, 2011a, 2011b, Mishra and Mondal, 2009, Chaabane et al, 2011c. However, in all such problems, although the radiative information was computed using the conventional RTE solvers and in terms of formulation and computational time, the solution of the energy equation by the LBM was encouraging.…”

“…Thus, development of methods, remain an ongoing phenomenon in the field of radiative heat transfer. For example, in a combined mode transient convection-radiation problem, the radiative information, which appears in the form of the divergence of radiative heat flux in the energy equation can be computed using various methods such as the Monte Carlo method (MCM) (Modest, 2003), the discrete transfer method (DTM) (Cumber, 1995, Mishra et al, 2003, the discrete ordinates method (DOM) (Jamaluddin and Smith, 1988), the finite-volume method (FVM) (Mishra et al, 2014a, Chui et al, 1992, Patankar and Chai, 2000, Mathur and Murthy, 1998, Kim, 2008, Kim and Baek, 2005, the collapsed dimension method (CDM) (Mishra et al, 2003), etc.However, in multi-dimensional geometry, in a combined mode problem, even with the FVM, the computational time becomes exorbitant (Mishra et al, 2014b). So, efforts toward development of efficient methods continue.…”