In this thesis, we present the results from tests of two global magnetohydrodynamic (MHD) codes: the University of New Hampshire's OPEN-GGCM model and the University of Michigan's BATS-R-US model. We investigate their consistency with the theory of adiabatic particle drift in the inner and middle magnetosphere. Since the Rice Convection Model (RCM) uses the adiabatic particle drift as one of its basic assumptions, positive results of the tests will help us to establish a better physical model of the magnetosphere and ionosphere by coupling the RCM with one of these global MHD models. An introduction to the two models, the theory for the adiabatic particle drift, and the results from tests of OPEN-GGCM and BATS-R-US models are presented. By tracking individual magnetic tubes and comparing the quantities such as particle number N and theoretical invariant PV5/3 integrated along these flux tubes in different times, we find results of both the OPEN-GGCM and BATS-R-US models suggest that the conservation of the adiabatic invariant is very poor when using low-resolution simulation grid. Another test of the OPEN-GGCM simulation with higher grid resolution shows some improvement in PV5/3 conservation.