Novel hybrid lattice Boltzmann technique with TVD characteristics for simulation of heat transfer and entropy generations of MHD and natural convection in a cavity

In the present study, a novel FD_LBM hybrid numerical method with total variation diminishing (TVD) characteristics is proposed to solve the famous problems of MagnetoHydroDynamics (MHD) and natural convection in a closed cavity. Here, the momentum and energy equations are carried out via lattice Boltzmann method (LBM) and FD techniques, respectively. To enhance the stability and performance of the finite difference scheme for higher Ra numbers, two renowned Superbee and Minmod flux limiter functions were used. The results for heat transfer and entropy generation features for a wide range of Rayleigh and Hartman numbers of 10(3) <= Ra <= 10(8) and 0 <= Ha <= 100 are presented. In addition for comparison purposes, two multiple relaxation time (MRT) and single relaxation time (SRT) algorithms presented in the open literature, were applied in the same case definitions. Not only the tests revealed an excellent agreement between the TVD method results and the published data, but they also proved that this new technique is numerically much more efficient and stable than the SRT and MRT methods, and hence one can assume the present method as a fantastic tool in the numerical solution of laminar convection problems.