Fluid-structure interaction simulations with a LES filtering approach in solids4Foam

The goal of this paper is to test solids4Foam, the fluid-structure interaction (FSI) toolbox developed for foam-extend (a branch of OpenFOAM), and assess its flexibility in handling more complex flows. For this purpose, we consider the interaction of an incompressible fluid described by a Leray model with a hyperelastic structure modeled as a Saint Venant-Kirchhoff material. We focus on a strongly coupled, partitioned fluid-structure interaction (FSI) solver in a finite volume environment, combined with an arbitrary Lagrangian-Eulerian approach to deal with the motion of the fluid domain. For the implementation of the Leray model, which features a nonlinear differential low-pass filter, we adopt a three-step algorithm called Evolve-Filter-Relax. We validate our approach against numerical data available in the literature for the 3D cross flow past a cantilever beam at Reynolds number 100 and 400

Lack of Reduction of Left Ventricular Mass in Treated Hypertension: The Strong Heart Study

BACKGROUND: Hypertensive left ventricular mass (LVM) is expected to decrease during antihypertensive therapy, based on results of clinical trials. METHODS AND RESULTS: We assessed 4‐year change of echocardiographic LVM in 851 hypertensive free‐living participants of the Strong Heart Study (57% women, 81% treated). Variations of 5% or more of the initial systolic blood pressure (SBP) and LVM were categorized for analysis. At baseline, 23% of men and 36% of women exhibited LV hypertrophy (LVH, P<0.0001). At the follow‐up, 3% of men and 10% of women had regression of LVH (P<0.0001 between genders); 14% of men and 15% of women, free of baseline LVH, developed LVH. There was an increase in LVM over time, more in men than in women (P<0.001). Participants whose LVM did not decrease had similar baseline SBP and diastolic BP, but higher body mass index (BMI), waist/hip ratio, heart rate (all P<0.008), and urinary albumin/creatinine excretion (P<0.001) than those whose LVM decreased. After adjusting for field center, initial LVM index, target BP, and kinship degree, lack of decrease in LVM was predicted by higher baseline BMI and urinary albumin/creatinine excretion, independently of classes of antihypertensive medications, and significant effects of older age, male gender, and percentage increase in BP over time. Similar findings were obtained in the subpopulation (n=526) with normal BP at follow‐up. CONCLUSIONS: In a free‐living population, higher BMI is associated with less reduction of hypertensive LVH; lack of reduction of LVM is independent of BP control and of types of antihypertensive treatment, but is associated with renal damage

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 a 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

A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations

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-α 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-α 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

A novel Large Eddy Simulation model for the Quasi-Geostrophic equations in a Finite Volume setting

We present a Large Eddy Simulation (LES) approach based on a nonlinear differential low-pass filter for the simulation of two-dimensional barotropic flows with under-refined meshes. For the implementation of such model, we choose a segregated three-step algorithm combined with a computationally efficient Finite Volume method. We assess the performance of our approach with the classical double-gyre wind forcing benchmark. The numerical experiments we present demonstrate that our nonlinear filter is an improvement over a linear filter since it is able to recover the four-gyre pattern of the time-averaged stream function even with extremely coarse meshes. In addition, our LES approach provides an average kinetic energy that compares well with the one computed with a Direct Numerical Simulation

A hybrid projection/data-driven reduced order model for the Navier-Stokes equations with nonlinear filtering stabilization

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≤Re≤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

A POD-Galerkin reduced order model for the Navier–Stokes equations in stream function-vorticity formulation

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier–Stokes equations in the stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients for the vorticity and stream function fields. In addition, for parametric studies we use a global POD basis space obtained from a database of time dependent full order snapshots related to sample points in the parameter space. We test the performance of our ROM strategy with the well-known vortex merger benchmark and a more complex case study featuring the geometry of the North Atlantic Ocean. Accuracy and efficiency are assessed for both time reconstruction and physical parameterization

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 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