This article proposes an efficient explicit numerical model with a relaxed stability condition for the simulation of heat, air and moisture transfer in porous material. Three innovative approaches are combined to solve the system of three partial differential equations. The Du Fort-Frankel scheme is used to solve the diffusion equation, providing an explicit scheme with an extended stability region. The two advection--diffusion equations are solved using both Scharfetter-Gummel numerical scheme for the space discretisation and the two-step Runge-Kutta method for the time variable. This combination enables to relax the stability condition by one order. The proposed numerical model is evaluated on three case studies. The first one considers quasi-linear coefficients to confirm the theoretical results by numerical computations. The stability condition is relaxed by a factor of 40 compared to the standard approach. The second case provides an analytical solution for weakly nonlinear problem. A very satisfactory accuracy is observed between the reference solution and the one provided by the numerical model. The last case study assumes more realistic application with nonlinear coefficients and Robin-type boundary conditions. The computational time is reduced 10 times by using the proposed model in comparison with the explicit Euler method.