| Abstract: |
| We propose a mathematical model to analyze the thermal behavior of extensive green roofs. This model is based on an energy balance for buildings with vegetation cover. The two-layer model includes a vegetation layer and a substrate layer, as well as the energy exchange between them. The unknowns in this problem are the temperatures of each layer which are described by a coupled system of two parabolic partial differential equations with Robin boundary conditions. One of the main feedback mechanisms is evapotranspiration, that is, the combined process of plant transpiration and substrate evaporation. The model takes into account the latent heat of fusion, due to the phase change of liquid water to ice or vice versa in the porous substrate. The modeling involves multivalued terms, and regularizing maximal monotone graphs is crucial to the mathematical treatment.
We approximate the solutions to the parabolic system of partial differential equations using the finite volume method with the Weighted Essentially Non-Oscillatory (WENO) technique for spatial reconstruction and the third-order SSPRK method for time integration. This is a joint work with L.Tello. |
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