Numerical method for solving coupled heat and mass transfer through walls for future integration into an urban climate model

Abstract

Numerous studies of hygrothermal transfers through walls have highlighted the impacts of this phenomenon on energy consumption and indoor conditions. However, urban scale models that aim to simulate weather conditions and urban heat island effects within cities neglect moisture transfer through walls. The objective of this paper is to propose a method for solving this phenomenon that could be integrated into an urban climate model. This kind of integration requires the numerical schemes to be adapted as well as the spatiotemporal scales. The proposed method is based on an Implicit/Explicit discretisation scheme and a decoupled numerical approach for solving. Numerical stability is ensured by reducing the time step in critical moments, which are detected by five tests. This method is validated by comparison with a reference model (Delphin ®), on several study cases using different wall compositions and climates. A mesh sensitivity analysis is performed and shows that low permeability walls require a finer mesh than walls made of highly hygroscopic or capillary active materials. Furthermore, the more layers there are in the wall, the finer the mesh size needs to be. This numerical method allowed a balance to be found between computational cost and accuracy level in accordance with the expectations for an urban climate model. The future integration of this method into an urban climate model will make it possible to carry out energy/climate simulations, including the hygrothermal behaviour of walls, and thus to study its impact at urban scale.