Many recent advances in novel solar cell technologies are based on charge separation in disordered semiconductor heterojunctions. In this work we use the Random Walk Numerical Simulation (RWNS) method to model the dynamics of electrons and holes in two disordered semiconductors in contact. Miller-Abrahams hopping rates and a tunnelling distance-dependent electron-hole annihilation mechanism are used to model transport and recombination, respectively. To test the validity of the model, three numerical "experiments" have been devised: (1) in the absence of constant illumination, charge separation has been quantified by computing surface photovoltage (SPV) transients. (2) By applying a continuous generation of electron-hole pairs, the model can be used to simulate a solar cell under steady-state conditions. This has been exploited to calculate open-circuit voltages and recombination currents for an archetypical bulk heterojunction solar cell (BHJ). (3) The calculations have been extended to nanostructured solar cells with inorganic sensitizers to study, specifically, non-ideality in the recombination rate. The RWNS model in combination with exponential disorder and an activated tunnelling mechanism for transport and recombination is shown to reproduce correctly charge separation parameters in these three "experiments". This provides a theoretical basis to study relevant features of novel solar cell technologies.