# An efficient numerical model for liquid water uptake in porous material and its parameter estimation

## TL;DR

This paper introduces an efficient numerical model using the Scharfetter-Gummel scheme to predict liquid water uptake in porous materials, validated against experiments and including parameter estimation for key coefficients.

## Contribution

It presents a novel application of the Scharfetter-Gummel scheme for modeling capillary adsorption with improved accuracy and computational efficiency.

## Key findings

- The model accurately predicts liquid uptake in bricks.
- The scheme offers relaxed stability conditions and reduced computational cost.
- Parameter estimation effectively calibrates moisture diffusivity and hydraulic conductivity.

## Abstract

The goal of this study is to propose an efficient numerical model for the predictions of capillary adsorption phenomena in a porous material. The Scharfetter-Gummel numerical scheme is proposed to solve an advection-diffusion equation with gravity flux. Its advantages such as accuracy, relaxed stability condition, and reduced computational cost are discussed along with the study of linear and nonlinear cases. The reliability of the numerical model is evaluated by comparing the numerical predictions with experimental observations of liquid uptake in bricks. A parameter estimation problem is solved to adjust the uncertain coefficients of moisture diffusivity and hydraulic conductivity.