Accurate numerical simulation of moisture front in porous material

When comparing measurements to numerical simulations of moisture transfer through porous materials a rush of the experimental moisture front is commonly observed in several works shown in the literature, with transient models that consider only the diffusion process. Thus, to overcome the discrepancies between the experimental and the numerical results, this paper proposes to include the moisture advection transfer in the governing equation. To solve the advection-diffusion or the so-called convection differential equation, it is first proposed two efficient numerical schemes whose efficiencies are investigated for both linear and nonlinear cases. The first scheme, SCHARFETTER–GUMMEL, presents a COURANT-FRIEDRICHS-LEWY (CFL) condition but it is more accurate and faster than the second one, the well-known CRANK–NICOLSON approach. Furthermore, the SCHARFETTER–GUMMEL scheme has the advantages of being well-balanced and asymptotically preserved. Then, to conclude, results of the convective moisture transfer problem obtained by means of the SCHARFETTER–GUMMEL numerical scheme are compared to experimental data from the literature. The inclusion of an advective term in the model may clearly lead to better results than purely diffusive models.