In the present study, a novel FD_LBM hybrid numerical method with TVD characteristics is proposed to solve the famous problems of MHD and natural convection in a closed cavity. Here, the momentum and energy equations are carried out via LBM and FD techniques, respectively. In order 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 and are presented. In addition for comparison purposes, two MRT and SRT algorithms presented in the open literature [1], 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.

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