# On the comparison of three numerical methods applied to building simulation: finite-differences, RC circuit approximation and a spectral method

## TL;DR

This paper compares three numerical methods—finite-differences, RC circuit approximation, and spectral method—for building physics simulations, evaluating their accuracy and computational efficiency across different heat and moisture transfer scenarios.

## Contribution

It provides a comparative analysis of the performance of three numerical methods in building physics, highlighting the spectral method's superior accuracy.

## Key findings

- Spectral method is the most accurate among the three.
- RC approach with few resistances is less accurate for temperature and vapor pressure.
- Finite-difference method offers a balance between accuracy and complexity.

## Abstract

Predictions of physical phenomena in buildings are carried out by using physical models formulated as a mathematical problem and solved by means of numerical methods, aiming at evaluating, for instance, the building thermal or hygrothermal performance by calculating distributions and fluxes of heat and moisture transfer. Therefore, the choice of the numerical method is crucial since it is a compromise among (i) the solution accuracy, (ii) the computational cost to obtain the solution and (iii) the complexity of the method implementation. An efficient numerical method enables to compute an accurate solution with a minimum computational run time (CPU). On that account, this article brings an investigation on the performance of three numerical methods. The first one is the standard and widely used finite-difference approach, while the second one is the so-called RC approach, which is a particular method brought to the building physics area by means of an analogy of electric circuits. The third numerical method is the spectral one, which has been recently proposed to solve nonlinear diffusive problems in building physics. The three methods are evaluated in terms of accuracy on the assessment of the dependent variable (temperature or vapor pressure) or of density of fluxes for three different cases: i) heat diffusion through a concrete slab, ii) moisture diffusion through an aerated concrete slab and iii) heat diffusion using measured temperatures as boundary conditions. Results highlight the spectral approach as the most accurate method. The RC based model with a few number of resistances does not provide accurate results for temperature and vapor pressure distributions neither to flux densities nor conduction loads.