The adiabatic invariants (M, J, Φ) and the related invariants (M, K, L*) have been established as effective coordinate systems for describing radiation belt dynamics at a theoretical level, and through numerical techniques, can be paired with in situ observations to order phase-space density. To date, methods for numerical techniques to calculate adiabatic invariants have focused on empirical models such the Tsyganenko models TS05, T96, and T89. In this work, we develop methods based on numerical integration and variable step size iteration for the calculation of adiabatic invariants, applying the method to the Lyon-Fedder-Mobarry (LFM) global magnetohydrodynamics (MHD) simulation code, with optional coupling to the Rice Convection Model (RCM). By opening the door to adiabatic invariant modeling with MHD magnetic fields, the opportunity for exploratory modeling work of radiation belt dynamics is enabled. Calculations performed using LFM are cross-referenced with the same code applied to the T96 and TS05 Tsyganenko models evaluated on the LFM grid. Important aspects of the adiabatic invariant calculation are reviewed and discussed, including (a) sensitivity to magnetic field model used, (b) differences in the problem between quiet and disturbed geomagnetic states, and (c) the selection of key parameters, such as the magnetic local time step size for drift shell determination. The rigorous development and documentation of this algorithm additionally acts as preliminary step for future thorough reassessment of in situ phase-space density results using alternative magnetic field models.