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We propose a regularization for reduced-order models (ROMs) of the quasi-geostrophic equations (QGE) to increase accuracy when the proper orthogonal decomposition (POD) modes retained to construct the reduced basis are insufficient to describe the system dynamics. Our regularization is based on the so-called BV-$\alpha $ model, which modifies the nonlinear term in the QGE and adds a linear differential filter for the vorticity. To show the effectiveness of the BV-$\alpha $ model for ROM closure, we compare the results computed by a POD-Galerkin ROM with and without regularization for the classical double-gyre wind forcing benchmark. Our numerical results show that the solution computed by the regularized ROM is more accurate, even when the retained POD modes account for a small percentage of the eigenvalue energy. Additionally, we show that, although computationally more expensive than the ROM with no regularization, the regularized ROM is still a competitive alternative to full-order simulations of the QGE.

The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order models that have successfully reduced the computational time for different applications in computational fluid dynamics while preserving accuracy: Dynamic Mode Decomposition (DMD), Hankel Dynamic Mode Decomposition (HDMD), and Proper Orthogonal Decomposition with Interpolation (PODI). The three methods are compared in terms of computational time and accuracy in the simulation of two well-known 2D benchmarks for mesoscale flow. The accuracy of the DMD and HDMD solutions deteriorates rather quickly as the forecast time window expands, although these methods are designed to predict the dynamics of a system. The reason is likely the strong nonlinearity in the benchmark flows. The PODI solution is accurate for the entire duration of the time interval of interest thanks to the use of interpolation with radial basis functions. This holds true also when the model features a physical parameter expected to vary in a given range, as is typically the case in weather prediction, and for preliminary results in 3D. • Application of data-driven ROMs for the simulation of mesoscale flow. • Use of ROMs for both system identification and prediction. • Parametric study including a physical parameter. • Validation against three well-know benchmarks for atmospheric modeling. [ABSTRACT FROM AUTHOR]

We develop a Reduced Order Model (ROM) for the Navier-Stokes equations with nonlinear filtering stabilization. Our approach, that can be interpreted as a Large Eddy Simulation model, combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method. The main novelty of our ROM lies in the use within the EFR algorithm of a nonlinear, deconvolution-based indicator function that identifies the regions of the domain where the flow needs regularization. The ROM we propose is a hybrid projection/data-driven strategy: a classical Proper Orthogonal Decomposition Galerkin projection approach for the reconstruction of the velocity and the pressure fields and a data-driven reduction method to approximate the indicator function used by the nonlinear differential filter. This data-driven technique is based on interpolation with Radial Basis Functions. We test the performance of our ROM approach on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0 ≤ R e ≤ 100. The accuracy of the ROM is assessed against results obtained with the full order model for velocity, pressure, indicator function and time evolution of the aerodynamics coefficients. • Development of a ROM for a Large Eddy Simulation algorithm called EFR. • Use of nonlinear indicator function both for the collection of the snapshots and in the reduced order model. • Combination of projection-based and data-driven strategies. • Validation against 2D and 3D benchmarks. [ABSTRACT FROM AUTHOR]

This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermo-mechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of reduced basis space. On the other hand, for the evaluation of the modal coefficients, we use two different methodologies: the one based on the Galerkin projection (G) and the other one based on Artificial Neural Network (ANN). We aim to compare POD-G and POD-ANN in terms of relevant features including errors and computational efficiency. In this context, both physical and geometrical parametrization are considered. We also carry out a validation of the Full Order Model (FOM) based on customized benchmarks in order to provide a complete computational pipeline. The framework proposed is applied to a relevant industrial problem related to the investigation of thermo-mechanical phenomena arising in blast furnace hearth walls. • Computational pipeline for fast and accurate thermo-mechanical FEM simulations. • Comparison between POD-Galerkin and POD-ANN model order reduction. • Parametric setting involving both physical properties and geometrical features. • Assessment of MOR approach with an industrial problem related to ironmaking process. [ABSTRACT FROM AUTHOR]

• Model order reduction for blood flows to enhance computational efficiency (real time). • Patient specific numerical simulations. • Efficient Haemodynamic simulations. Left ventricular assist devices (LVADs) are used to provide haemodynamic support to patients with critical cardiac failure. Severe complications can occur because of the modifications of the blood flow in the aortic region. In this work, the effect of a continuous flow LVAD device on the aortic flow is investigated by means of a non-intrusive reduced order model (ROM) built using the proper orthogonal decomposition with interpolation (PODI) method based on radial basis functions (RBF). The full order model (FOM) is represented by the incompressible Navier-Stokes equations discretized by using a Finite Volume (FV) technique, coupled with three-element Windkessel models to enforce outlet boundary conditions in a multi-scale approach. A patient-specific framework is proposed: a personalized geometry reconstructed from Computed Tomography (CT) images is used and the individualization of the coefficients of the three-element Windkessel models is based on experimental data provided by the Right Heart Catheterization (RHC) and Echocardiography (ECHO) tests. At FOM level, we also consider the pre-surgery configuration in order to further validate the predictive capabilities of the model in several contexts. The ROM has been tested by considering a parametric setting with respect to the LVAD flow, which is a crucial parameter of the problem. We consider a parameter range that covers typical clinical values. The accuracy of the ROM is assessed against results obtained with the FOM both for primal, velocity and pressure, and derived quantities, wall shear stress (WSS). Finally, we briefly discuss the efficiency of our ROM approach. [ABSTRACT FROM AUTHOR]

• Development of a POD-Galerkin ROM for an algorithm (EF) implementing the Leray model. • Combination of a ROM spatial filter using an explicit lengthscale with a FV method. • Use of spatial filtering both for the collection of the snapshots and in the reduced order model. • Computation of the pressure field at ROM level. • Validation against 2D and 3D benchmarks and parametric study for filtering radius. We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for an implementation of the Leray model that combines a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. The main novelty of the proposed approach relies in applying spatial filtering both for the collection of the snapshots and in the reduced order model, as well as in considering the pressure field at reduced level. In both steps of the EF algorithm, velocity and pressure fields are approximated by using different POD basis and coefficients. For the reconstruction of the pressures fields, we use a pressure Poisson equation approach. We test our ROM on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0 ≤ R e ≤ 100. The accuracy of the reduced order model is assessed against results obtained with the full order model. For the 2D case, a parametric study with respect to the filtering radius is also presented. [ABSTRACT FROM AUTHOR]

The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations needs to be studied. In this context, we develop a non-intrusive data-driven reduced order model (ROM) built using the proper orthogonal decomposition with interpolation (PODI) method for Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations. The main novelties of the proposed approach rely in (i) the combination of ROM and FV methods, (ii) a numerical sensitivity analysis of the ROM accuracy with respect to the number of POD modes and to the cardinality of the training set and (iii) a parametric study with respect to the Stokes number. We test our ROM on the fluidized bed benchmark problem. The accuracy of the ROM is assessed against results obtained with the FOM both for Eulerian (the fluid volume fraction) and Lagrangian (position and velocity of the particles) quantities. We also discuss the efficiency of our ROM approach. • Development of a data-driven ROM for a CFD-DEM framework. • Combination of ROM and FV methods for multiphysics problems. • Extensive numerical investigation of the ROM error. • Use of local and global PODI techniques for physical parametrization. • Validation against a relevant benchmark for pharmaceutical industry. [ABSTRACT FROM AUTHOR]