# An adaptive simulation of nonlinear heat and moisture transfer as a boundary value problem

## TL;DR

This paper introduces an innovative numerical simulation approach for nonlinear heat and moisture transfer in porous materials, transforming the problem into a boundary value problem solved efficiently with adaptive collocation methods, validated through case studies.

## Contribution

It proposes a novel time discretization method that converts the problem into a boundary value problem, enabling more efficient and accurate simulations of diffusion in porous materials.

## Key findings

- Effective treatment of nonlinearities and interfaces
- High-order adaptive methods improve accuracy
- Good agreement with experimental data

## Abstract

This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through porous building materials. Traditionally, by using the finite-difference approach, the discretization follows the Method Of Lines (MOL), when the problem is first discretized in space to obtain a large system of coupled Ordinary Differential Equations (ODEs). Thus, this paper proposes to change this viewpoint. First, we discretize in time to obtain a small system of coupled ODEs, which means instead of having a Cauchy (Initial Value) Problem (IVP), we have a Boundary Value Problem (BVP). Fortunately, BVPs can be solved efficiently today using adaptive collocation methods of high order. To demonstrate the benefits of this new approach, three case studies are presented, in which one of them is compared with experimental data. The first one considers nonlinear heat and moisture transfer through one material layer while the second one considers two material layers. Results show how the nonlinearities and the interface between materials are easily treated, by reasonably using a fourth-order adaptive method. Finally, the last case study compares numerical results with experimental measurements, showing a good agreement.