A mixed POD–PGD approach to parametric thermal impervious soil modeling: Application to canyon streets

Abstract

Numerical simulation is a powerful tool for assessing the causes of an Urban Heat Island (UHI) effect or quantifying the impact of mitigation solutions on local climatic conditions. However, the numerical cost associated with such a tool, which may seem low for a section of mesh within the district geometric model, is quite significant at the scale of an entire district. Today, the main challenge consists of achieving both a proper representation of the physical phenomena and a critical reduction in the numerical costs of running simulations. This paper presents a combined parametric urban soil model that accurately reproduces thermal heat flux exchanges between the soil and the urban environment with a reduced computation time. For this purpose, the use of a combination of two reduced-order methods is proposed herein: the Proper Orthogonal Decomposition (POD) method, and the Proper Generalized Decomposition (PGD) method. The developed model is applied to two case studies in order to establish a practical evaluation: an open area independent of the influences of the surrounding surface, namely a parking lot, and a theoretical urban scene with two canyon streets. The mean surface temperature reduction error remains below 0.52˝C for a cut computational cost of 80%.

Parametric PGD model used with orthogonal polynomials to assess efficiently the building's envelope thermal performance

“…The enrichment process of the PGD basis stops when the ǫ criterion, defined by the user, is reached [11]. Details on the alternating directions strategy equations and algorithms for a similar problem can be found on [3]. For further details on the method and its developments, the interested reader may refer to [11,15].…”

“…As in the theoretical example, the POD basis is the most accurate one for N ∈ [2,8], if the full data-set is used for the training period. However if only a part of the data is available, the Chebyshev and Legendre approximation basis are more efficient for N ∈ [2,3]. The POD basis trained with half of the cycles seems to be as efficient as the one built with the full training data-set for N ∈ [4,8].…”

“…Applied to urban soil heat transfer modeling, this model reduction method has shown its efficiency [3]. A cut computational cost of 80% was observed for a mean surface temperature error below 0.52 • C. Applied to building wall heat transfer modeling, the PGD parametric model computes the solution 100 times faster than a classical numerical method [4].…”

Assessing the wall energy efficiency design under climate change using POD reduced order model

“…In [26], the wall energy efficiency is computed according to the thickness and thermal diffusivity of the layers. A parametric solution is proposed in [27] to compute the heat transfer in soil within the urban environment. In [28], the two-dimensional heat transfer is solved for different climatic boundary conditions.…”

“…In the works related to the POD [23,24,28], the solution is not parametric per se. Recent works [27,28] investigate the accuracy of the POD basis by using the same reduced basis for space for computations with different parameters. However, the accuracy of this approach can be very low in some cases as noted in [23].…”