Fully coupled algorithm for heat and water transport – Estimation of non-linear parameters based on the experimental data

We solve the problem of coupled heat conduction and water transport in bentonite with water present in vapour and adsorbed form in a non-equilibrium state. The problem is governed by a system of two parabolic PDE and one ODE. Most of the coefficients are non-linear functions, defined either by underlying physical phenomena or empirically. We present a numerical scheme using FEM with linear base functions, implicit time discretization, and simple iterations for the non-linear terms. The model is verified against experiments (one 1D and one 3D) and we demonstrate the use of optimization algorithm for parameter calibration. Some of the parameters could be estimated successfully while others with limited confidence, which is explained by the particular character of the non-linear parameter dependence and resulting small sensitivity of the model on some parameters.