Models of development of lattice preferred orientation (LPO) of crystals aggregates in convective flow are necessary to interpret the anisotropic seismic signature of the Earth's upper mantle. For that purpose we previously developed a model of LPO evolution in olivine aggregates by plastic deformation and dynamic recrystallization by subgrain rotation and grain-boundary migration. This paper presents a refined version of that model, called D-Rex (for dynamic recrystallization-induced LPO), a public version of which is made available on our web site. The code displays two new features: (1) enstatite is incorporated in the aggregates and (2) grain-boundary sliding (GBS) of small grains is taken into account. Enstatite is incorporated on the assumption of no direct interaction with olivine. The fast (a-)axis of enstatite grains tend to be parallel to the slow (c-)axis of olivine, which dilutes the total anisotropy. Grain boundary sliding is included using a threshold dimensionless volume fraction χ, defined as the ratio of the initial size of the grains over the size for which GBS is the dominant mechanism of deformation. Grains with a dimensionless volume smaller than χ do not rotate by plastic deformation and their strain energy is set to zero. Comparison with torsion experiments at very large strain constrains the threshold dimensionless volume to 0.3 ± 0.1. The incorporation of grain-boundary sliding prevents the LPO from becoming singular at large strains and yields more realistic predictions. Our kinematic formalism and the model's semi-analytical character insures that it is fast, robust and stable. It can be applied efficiently to arbitrary 3-D convective flows.