Coupled Lattice Boltzmann and Meshless Simulation of Natural Convection in the Presence of Volumetric Radiation

Abstract

In this work, the coupled lattice Boltzmann and direct collocation meshless (LB–DCM) method is introduced to solve the natural convection in the presence of volumetric radiation in irregular geometries. LB–DCM is a hybrid approach based on a common multiscale Boltzmann-type model. Separate particle distribution functions with multirelaxation time (MRT) and lattice Bhatnagar–Gross–Krook (LBGK) models are used to calculate the flow field and the thermal field, respectively. The radiation transfer equation is computed using the meshless method with moving least-squares (MLS) approximation. The LB–DCM code is first validated by the case of coupled convection–radiation flows in a square cavity. Comparisons show that this combined method is accurate and efficient. Then, the coupled convective and radiative heat transfer in two complex geometries are simulated at various parameters, such as eccentricity, Rayleigh number, and convection–radiation parameter. Numerical results show that the LB–DCM combination is a potential technique for the multifield coupling models, especially with the curved boundary.