# A new model for simulating heat, air and moisture transport in porous building materials

## TL;DR

This paper introduces a comprehensive mathematical and numerical model for simulating heat, air, and moisture transfer in porous building materials, achieving accurate results with significantly reduced computational effort.

## Contribution

The work develops an innovative numerical scheme combining Du Fort-Frankel, Runge-Kutta, and Scharfetter-Gummel methods to efficiently simulate coupled heat, air, and moisture transfer.

## Key findings

- Model predicts heat, air, moisture transfer accurately.
- Simulation is approximately 16 times faster than standard methods.
- Validated against experimental data with good agreement.

## Abstract

This work presents a detailed mathematical model combined with an innovative efficient numerical model to predict heat, air and moisture transfer through porous building materials. The model considers the transient effects of air transport and its impact on the heat and moisture transfer. The achievement of the mathematical model is detailed in the continuity of Luikov's work. A system composed of two advection-diffusion differential equations plus one exclusively diffusion equation is derived. The main issue to take into account the transient air transfer arises in the very small characteristic time of the transfer, implying very fine discretisation. To circumvent these difficulties, the numerical model is based on the Du Fort-Frankel explicit and unconditionally stable scheme for the exclusively diffusion equation. It is combined with a two-step Runge-Kutta scheme in time with the Scharfetter-Gummel numerical scheme in space for the coupled advection-diffusion equations. At the end, the numerical model enables to relax the stability condition, and, therefore, to save important computational efforts. A validation case is considered to evaluate the efficiency of the model for a nonlinear problem. Results highlight a very accurate solution computed about 16 times faster than standard approaches. After this numerical validation, the reliability of the mathematical model is evaluated by comparing the numerical predictions to experimental observations. The latter is measured within a multi-layered wall submitted to a sudden increase of vapor pressure on the inner side and driven climate boundary conditions on the outer side. A very satisfactory agreement is noted between the numerical predictions and experimental observations indicating an overall good reliability of the proposed model.