MFIX (Multiphase Flow with Interphase eXchanges) is a general-purpose hydrodynamic model for describing chemical reactions and heat transfer in dense or dilute fluid-solids flows, which typically occur in energy conversion and chemical processing reactors. The calculations give time-dependent information on pressure, temperature, composition, and velocity distributions in the reactors. The theoretical basis of the calculations is described in the MFIX Theory Guide. Installation of the code, setting up of a run, and post-processing of results are described in MFIX User`s manual. Work was started in April 1996 to increase the execution speed and accuracy of the code, which has resulted in MFIX 2.0. To improve the speed of the code the old algorithm was replaced by a more implicit algorithm. In different test cases conducted the new version runs 3 to 30 times faster than the old version. To increase the accuracy of the computations, second order accurate discretization schemes were included in MFIX 2.0. Bubbling fluidized bed simulations conducted with a second order scheme show that the predicted bubble shape is rounded, unlike the (unphysical) pointed shape predicted by the first order upwind scheme. This report describes the numerical technique used in MFIX 2.0.