A formal re-definition of the hydrodynamic equations for a compressible uniaxial nematic fluid in the presence of dispersed particles is presented, which is particularly amenable to computational treatment. Starting from the Parodi-Foster formulation of nematodynamics equations, it is shown that a functional formulation of the time evolution equations can be obtained which clearly separate conservative and dissipative terms. A simplified discretization scheme is also proposed, which leads to pseudo-particle representation of the fluid in combination with a standard description of the dispersed particles motion.