A combination of the Direct Numerical Simulation (DNS) with the Immersed Boundary (IB) method has been developed to solve the momentum and heat transfer equations for the computation of thermal convection in particulate flows. This numerical method makes use of a finite difference method in and uses a regular Eulerian grid to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the solid particles, a second particle-based Lagrangian grid is used, which tracks all the particles, and a force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between the particulate phase and fluid phase. The numerical methods presented have been validated by comparing the results of the simulation with similar numerical results obtained by others. Among the advantages of this computational method is that it may be used for the determination, stipulation and validation of boundary conditions in particulate flows that may be used with larger Eulerian codes.

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