In this paper, we introduce a low-cost, high-order stabilized method for the numerical solution of incompressible flow problems. This is a particular type of projection-stabilized method where each targeted operator, such as the pressure gradient or the convection, is stabilized by least-squares terms added to the Galerkin formulation. The main methodological originality is that we replace the projection-stabilized structure by an interpolation-stabilized structure, with reduced computational cost for some choices of the interpolation operator. This stabilization has one level, in the sense that it is defined on a single mesh. We prove the stability of our formulation by means of a specific inf–sup condition, which is the main technical innovation of our paper. We perform a convergence and error estimates analysis, proving the optimal order of accuracy of our method. We include some numerical tests that confirm our theoretical expectations.

Gurney flaps (GFs) and microtabs (MTs) are two of the most frequently used passive flow control devices on wind turbines. They are small tabs situated close to the airfoil trailing edge and normal to the surface. A study to find the most favorable dimension and position to improve the aerodynamic performance of an airfoil is presented herein. Firstly, a parametric study of a GF on a S810 airfoil and an MT on a DU91(2)250 airfoil was carried out. To that end, 2D computational fluid dynamic simulations were performed at Re = 10⁶ based on the airfoil chord length and using RANS equations. The GF and MT design parameters resulting from the computational fluid dynamics (CFD) simulations allowed the sizing of these passive flow control devices based on the airfoil’s aerodynamic performance. In both types of flow control devices, the results showed an increase in the lift-to-drag ratio for all angles of attack studied in the current work. Secondly, from the data obtained by means of CFD simulations, a regular function using the proper orthogonal decomposition (POD) was used to build a reduced order method. In both flow control cases (GFs and MTs), the recursive POD method was able to accurately and very quickly reproduce the computational results with very low computational cost.

Currently, there is a lack of accurate simulation tools for the thermal performance modeling of courtyards due to their intricate thermodynamics. Machine Learning (ML) models have previously been used to predict and evaluate the structural performance of buildings as a means of solving complex mathematical problems. Nevertheless, the microclimatic conditions of the building surroundings have not been as thoroughly addressed by these methodologies. To this end, in this paper, the adaptation of ML techniques as a more comprehensive methodology to fill this research gap, covering not only the prediction of the courtyard microclimate but also the interpretation of experimental data and pattern recognition, is proposed. Accordingly, based on the climate zoning and aspect ratios of 32 monitored case studies located in the South of Spain, the Support Vector Regression (SVR) method was applied to predict the measured temperature inside the courtyard. The results provided by this strategy showed good accuracy when compared to monitored data. In particular, for two representative case studies, if the daytime slot with the highest urban overheating is considered, the relative error is almost below 0.05%. Additionally, values for statistical parameters are in good agreement with other studies in the literature, which use more computationally expensive CFD models and show more accuracy than existing commercial tools.