The two-fluid model with kinetic theory of granular flow is implemented into the open source CFD package OpenFOAM. The effect of total variation diminishing (TVD) convection schemes is investigated by simulating two bubbling fluidized beds. Five TVD schemes are employed to discretize the convection terms of phase velocity and solid volume fraction. Simulated results of the two test cases give reasonable agreement with the experimental data in the literature. For the discretization of the phase velocity convection terms, the five schemes give quite similar time-averaged radial profiles of particle axial velocity. The predicted bubbles in the bed with a central jet are not influenced by the different schemes. For the discretization of the solid volume fraction convection terms, the limitedLinear01, Sweby01 and vanLeer01 schemes give the converged and reasonable solutions, whereas the SuperBee01 and MUSCLO1 schemes diverge the solutions. When using the faceLimited gradient scheme the convection scheme becomes more diffusive. (C) 2014 Elsevier Ltd. All rights reserved.