A POD-Galerkin reduced order model for a LES filtering approach

We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for a Leray model. For the implementation of the model, we combine 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 <= Re <= 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.Comment: 29 pages, 16 figures, 9 table

Pressure stabilization strategies for a LES filtering Reduced Order Model

We present a stabilized POD-Galerkin reduced order method (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. In both steps of the EF algorithm, velocity and pressure fields are approximated using different POD basis and coefficients. To achieve pressure stabilization, we consider and compare two strategies: the pressure Poisson equation and the supremizer enrichment of the velocity space. We show that the evolve and filtered velocity spaces have to be enriched with the supremizer solutions related to both evolve and filter pressure fields in order to obtain stable and accurate solutions with the supremizer enrichment method. We test our ROM approach on 2D unsteady flow past a cylinder at Reynolds number 0 <= Re <= 100. We find that both stabilization strategies produce comparable errors in the reconstruction of the lift and drag coefficients, with the pressure Poisson equation method being more computationally efficient.Comment: 18 pages, 4 figures, 3 tables. arXiv admin note: substantial text overlap with arXiv:2009.1359

A comparative computational study of different formulations of the compressible Euler equations for mesoscale atmospheric flows in a finite volume framework

We consider three conservative forms of the mildly compressible Euler equations, called CE1, CE2 and CE3, with the goal of understanding which leads to the most accurate and robust pressure-based solver in a finite volume environment. Forms CE1 and CE2 are both written in density, momentum, and specific enthalpy, but employ two different treatments of the buoyancy and pressure gradient terms: for CE1 it is the standard pressure splitting implemented in open-source finite volume solvers (e.g., OpenFOAM), while for CE2 it is the typical pressure splitting found in computational atmospheric studies. Form CE3 is written in density, momentum, and potential temperature, with the buoyancy and pressure terms addressed as in CE2. For each formulation, we adopt a computationally efficient splitting approach. The three formulations are thoroughly assessed and compared through six benchmark tests involving dry air flow over a flat terrain or orography. We found that all three models are able to provide accurate results for the tests with a flat terrain, although the solvers based on the CE2 and CE3 forms are more robust. As for the mountain tests, CE1 solutions become unstable, while the CE2 and CE3 models provide results in very good agreement with data in the literature, the CE3 model being the most accurate. Hence, the CE3 model is the most accurate, reliable, and robust for the simulation of mesoscale atmospheric flows when using a pressure-based approach and space discretization by a finite volume method.Comment: 23 pages, 15 figures, 3 table

A Comparison of Data-Driven Reduced Order Models for the Simulation of Mesoscale Atmospheric Flow

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 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

Consistency of the full and reduced order models for evolve-filter-relax regularization of convection-dominated, marginally-resolved flows

Numerical stabilization is often used to eliminate (alleviate) the spurious oscillations generally produced by full order models (FOMs) in under-resolved or marginally-resolved simulations of convection-dominated flows. In this article, we investigate the role of numerical stabilization in reduced order models (ROMs) of marginally-resolved, convection-dominated incompressible flows. Specifically, we investigate the FOM–ROM consistency, that is, whether the numerical stabilization is beneficial both at the FOM and the ROM level. As a numerical stabilization strategy, we focus on the evolve-filter-relax (EFR) regularization algorithm, which centers around spatial filtering. To investigate the FOM-ROM consistency, we consider two ROM strategies: (i) the EFR-noEFR, in which the EFR stabilization is used at the FOM level, but not at the ROM level; and (ii) the EFR-EFR, in which the EFR stabilization is used both at the FOM and at the ROM level. We compare the EFR-noEFR with the EFR-EFR in the numerical simulation of a 2D incompressible flow past a circular cylinder in the convection-dominated, marginally-resolved regime. We also perform model reduction with respect to both time and Reynolds number. Our numerical investigation shows that the EFR-EFR is more accurate than the EFR-noEFR, which suggests that FOM-ROM consistency is beneficial in convection-dominated, marginally-resolved flows

A Non-Intrusive Data-Driven Reduced Order Model for Parametrized CFD-DEM Numerical Simulations

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

Advances in reduced order methods for parametric industrial problems in computational fluid dynamics

Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems

Consistency of the full and reduced order models for evolve-filter-relax regularization of convection-dominated, marginally-resolved flows

Numerical stabilization is often used to eliminate (alleviate) the spurious oscillations generally produced by full order models (FOMs) in under-resolved or marginally-resolved simulations of convection-dominated flows. In this article, we investigate the role of numerical stabilization in reduced order models (ROMs) of marginally-resolved, convection-dominated incompressible flows. Specifically, we investigate the FOM-ROM consistency, that is, whether the numerical stabilization is beneficial both at the FOM and the ROM level. As a numerical stabilization strategy, we focus on the evolve-filter-relax (EFR) regularization algorithm, which centers around spatial filtering. To investigate the FOM-ROM consistency, we consider two ROM strategies: (i) the EFR-noEFR, in which the EFR stabilization is used at the FOM level, but not at the ROM level; and (ii) the EFR-EFR, in which the EFR stabilization is used both at the FOM and at the ROM level. We compare the EFR-noEFR with the EFR-EFR in the numerical simulation of a 2D incompressible flow past a circular cylinder in the convection-dominated, marginally-resolved regime. We also perform model reduction with respect to both time and Reynolds number. Our numerical investigation shows that the EFR-EFR is more accurate than the EFR-noEFR, which suggests that FOM-ROM consistency is beneficial in convection-dominated, marginally-resolved flows