In this paper, we prove uniform error bounds for proper orthogonal decomposition (POD) reduced or... more In this paper, we prove uniform error bounds for proper orthogonal decomposition (POD) reduced order modeling (ROM) of Burgers equation, considering difference quotients (DQs), introduced in Kunisch and Volkwein (Numer Math 90(1):117–148, 2001). In particular, we study the behavior of the DQ ROM error bounds by considering $$L^2(\Omega )$$ L 2 ( Ω ) and $$H^1_0(\Omega )$$ H 0 1 ( Ω ) POD spaces and $$l^{\infty }(L^2)$$ l ∞ ( L 2 ) and natural-norm errors. We present some meaningful numerical tests checking the behavior of error bounds. Based on our numerical results, DQ ROM errors are several orders of magnitude smaller than noDQ ones (in which the POD is constructed in a standard way, i.e., without the DQ approach) in terms of the energy kept by the ROM basis. Further, noDQ ROM errors have an optimal behavior, while DQ ROM errors, where the DQ is added to the POD process, demonstrate an optimality/super-optimality behavior. It is conjectured that this possibly occurs because the DQ...
We introduce improved Reduced Order Models (ROM) for convection-dominated flows. These non-linear... more We introduce improved Reduced Order Models (ROM) for convection-dominated flows. These non-linear closure models are inspired from successful numerical stabilization techniques used in Large Eddy Simulations (LES), such as Local Projection Stabilization (LPS), applied to standard models created by Proper Orthogonal Decomposition (POD) of flows with Galerkin projection. The numerical analysis of the fully Navier-Stokes discretization for the proposed new POD-ROM is presented, by mainly deriving the corresponding error estimates. Also, we suggest an efficient practical implementation of the stabilization term, where the stabilization parameter is approximated by the Discrete Empirical Interpolation Method (DEIM).
Gurney flaps (GFs) and microtabs (MTs) are two of the most frequently used passive flow control d... more 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 si...
In this paper, we prove uniform error bounds for proper orthogonal decomposition (POD) reduced or... more In this paper, we prove uniform error bounds for proper orthogonal decomposition (POD) reduced order modeling (ROM) of Burgers equation, considering difference quotients (DQs), introduced in Kunisch and Volkwein (Numer Math 90(1):117–148, 2001). In particular, we study the behavior of the DQ ROM error bounds by considering $$L^2(\Omega )$$ L 2 ( Ω ) and $$H^1_0(\Omega )$$ H 0 1 ( Ω ) POD spaces and $$l^{\infty }(L^2)$$ l ∞ ( L 2 ) and natural-norm errors. We present some meaningful numerical tests checking the behavior of error bounds. Based on our numerical results, DQ ROM errors are several orders of magnitude smaller than noDQ ones (in which the POD is constructed in a standard way, i.e., without the DQ approach) in terms of the energy kept by the ROM basis. Further, noDQ ROM errors have an optimal behavior, while DQ ROM errors, where the DQ is added to the POD process, demonstrate an optimality/super-optimality behavior. It is conjectured that this possibly occurs because the DQ...
We introduce improved Reduced Order Models (ROM) for convection-dominated flows. These non-linear... more We introduce improved Reduced Order Models (ROM) for convection-dominated flows. These non-linear closure models are inspired from successful numerical stabilization techniques used in Large Eddy Simulations (LES), such as Local Projection Stabilization (LPS), applied to standard models created by Proper Orthogonal Decomposition (POD) of flows with Galerkin projection. The numerical analysis of the fully Navier-Stokes discretization for the proposed new POD-ROM is presented, by mainly deriving the corresponding error estimates. Also, we suggest an efficient practical implementation of the stabilization term, where the stabilization parameter is approximated by the Discrete Empirical Interpolation Method (DEIM).
Gurney flaps (GFs) and microtabs (MTs) are two of the most frequently used passive flow control d... more 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 si...
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Papers by Tomás Chacón Rebollo