Two complementary approaches are developed to model mode competition， frequency tuning， and radiation power in binary terahertz quantum cascade （THz-QCL） arrays. The first approach is based on a temporal coupled-mode theory model incorporating nonlinear gain， which efficiently simulates the evolution of the intracavity electric field amplitudes and gains after lasing onset. This approach reproduces the mode competition and frequency tuning behaviors observed in experiments， and predicts the maximum continuous tuning range of the binary THz-QCL arrays. The second approach is based on a time-domain finite-element method incorporating both nonlinear gain and gain frequency dispersion. This approach explicitly includes the detailed cavity geometry， thereby enabling accurate simulations of radiation power in addition to mode competition and frequency tuning. The simulated results are in good agreement with the experimental measurements， yielding errors of 9% in the frequency tuning range and approximately 50% in the radiation power. The combined use of these two approaches provides an effective framework for optimizing the frequency tuning range and radiation power of binary coupled laser arrays. Furthermore， these two approaches are applicable not only to binary THz-QCL arrays but can also be extended to general coupled Class-A lasers with negligible gain-response delay.