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Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady flows past moving bodies, such as flapping wings is scarce. Earlier studies mostly relied on transferring to a body attached frame of reference which is restrictive towards handling multiple moving bodies or deforming structures. Hence, in the present work, an immersed boundary aware framework has been explored for developing surrogate models for unsteady flows past moving bodies. Specifically, simultaneous pressure recovery and velocity reconstruction from Immersed boundary method (IBM) simulation data has been investigated. While, efficacy of velocity reconstruction has been tested against the fine resolution IBM data, as a step further, the pressure recovered was compared with that of an arbitrary Lagrange Eulerian (ALE) based solver. Under this framework, two PINN variants, (i) a moving-boundary-enabled standard Navier-Stokes based PINN (MB-PINN), and, (ii) a moving-boundary-enabled IBM based PINN (MB-IBM-PINN) have been formulated. A fluid-solid partitioning of the physics losses in MB-IBM-PINN has been allowed, in order to investigate the effects of solid body points while training. This enables MB-IBM-PINN to match with the performance of MB-PINN under certain loss weighting conditions. MB-PINN is found to be superior to MB-IBM-PINN when {\it a priori} knowledge of the solid body position and velocity are available. To improve the data efficiency of MB-PINN, a physics based data sampling technique has also been investigated. It is observed that a suitable combination of physics constraint relaxation and physics based sampling can achieve a model performance comparable to the case of using all the data points, under a fixed training budget.

The Reynolds-Averaged Navier-Stokes (RANS) approach remains a backbone for turbulence modeling due to its high cost-effectiveness. Its accuracy is largely based on a reliable Reynolds stress anisotropy tensor closure model. There has been an amount of work aiming at improving traditional closure models, while they are still not satisfactory to some complex flow configurations. In recent years, advances in computing power have opened up a new way to address this problem: the machine-learning-assisted turbulence modeling. In this paper, we employ neural networks to fully predict the Reynolds stress anisotropy tensor of turbulent channel flows at different friction Reynolds numbers, for both interpolation and extrapolation scenarios. Several generic neural networks of Multi-Layer Perceptron (MLP) type are trained with different input feature combinations to acquire a complete grasp of the role of each parameter. The best performance is yielded by the model with the dimensionless mean streamwise velocity gradient $\alpha$, the dimensionless wall distance $y^+$ and the friction Reynolds number $\mathrm{Re}_\tau$ as inputs. A deeper theoretical insight into the Tensor Basis Neural Network (TBNN) clarifies some remaining ambiguities found in the literature concerning its application of Pope's general eddy viscosity model. We emphasize the sensitivity of the TBNN on the constant tensor $\textbf{T}^{*(0)}$ upon the turbulent channel flow data set, and newly propose a generalized $\textbf{T}^{*(0)}$, which considerably enhances its performance. Through comparison between the MLP and the augmented TBNN model with both $\{\alpha, y^+, \mathrm{Re}_\tau\}$ as input set, it is concluded that the former outperforms the latter and provides excellent interpolation and extrapolation predictions of the Reynolds stress anisotropy tensor in the specific case of turbulent channel flow., Comment: 35 pages, 10 figures

Mapping near-field pollutant concentration is essential to track accidental toxic plume dispersion in urban areas. By solving a large part of the turbulence spectrum, large-eddy simulations (LES) have the potential to accurately represent pollutant concentration spatial variability. Finding a way to synthesize this large amount of information to improve the accuracy of lower-fidelity operational models (e.g. providing better turbulence closure terms) is particularly appealing. This is a challenge in multi-query contexts, where LES become prohibitively costly to deploy to understand how plume flow and tracer dispersion change with various atmospheric and source parameters. To overcome this issue, we propose a non-intrusive reduced-order model combining proper orthogonal decomposition (POD) and Gaussian process regression (GPR) to predict LES field statistics of interest associated with tracer concentrations. GPR hyperpararameters are optimized component-by-component through a maximum a posteriori (MAP) procedure informed by POD. We provide a detailed analysis of the reducedorder model performance on a two-dimensional case study corresponding to a turbulent atmospheric boundary-layer flow over a surface-mounted obstacle. We show that near-source concentration heterogeneities upstream of the obstacle require a large number of POD modes to be well captured. We also show that the component-by-component optimization allows to capture the range of spatial scales in the POD modes, especially the shorter concentration patterns in the high-order modes. The reduced-order model predictions remain acceptable if the learning database is made of at least fifty to hundred LES snapshot providing a first estimation of the required budget to move towards more realistic atmospheric dispersion applications.

Cardiac disease and clinical intervention may both lead to an increased risk for thrombosis events due to modified blood flow in the heart, and thereby a change in the mechanical stimuli of blood cells passing through the chambers of the heart. Specifically, the degree of platelet activation is influenced by the level and type of mechanical stresses in the blood flow. Here we analyze the blood flow in the left ventricle of the heart through a computational model constructed from patient-specific data. The blood flow in the ventricle is modeled by the Navier-Stokes equations, and the flow through the mitral valve by a parameterized model which represents the projected opening of the valve. A finite element method is used to solve the equations, from which a simulation of the velocity and pressure of the blood flow is constructed. A triple decomposition of the velocity gradient tensor is then used to distinguish between rigid body rotational flow, irrotational straining flow, and shear flow. The triple decomposition enables the separation of three fundamentally different flow structures, each generating a distinct type of mechanical stimulus on the blood cells in the flow. We compare the results to simulations where a mitral valve clip intervention is modelled, which leads to a significant modification of the ventricular flow. It was found that the shear in the simulation cases treated with clips increased more compared to the untreated case than the rotation and strain did. A decrease in valve opening area of 64 % in one of the cases led to a 90 % increase in rotation and strain, but a 150 % increase in shear. The computational analysis suggests a process for patient-specific simulation of clinical interventions in the heart with a detailed analysis of the resulting blood flow, which could support clinical risk assessment with respect to platelet activation and thrombosis events., Comment: The following article has been submitted to Frontiers in Physiology

International audience

International audience; In pollutant dispersion problems, mapping concentrations in the first tens or hundreds of meters from the source still remains a modelling challenge. Large-eddy simulations (LES) are able to represent time and space variability of turbulent atmospheric flow, which is of prime importance to assess public short-term exposure. However, they remain far from real time and subject to uncertainties, in particular to parametric uncertainties associated with the large-scale atmospheric forcing and the emission source position. In this work, we show that an efficient and accurate metamodel of the tracer concentration information provided by LES and encapsulating their associated uncertainties can be built using appropriate statistical tools combining machine learning and principal component analysis. We present a proof-ofconcept study based on a simplified but representative flow configuration (two-dimensional flow around a surfacemounted cube) using the AVBP LES solver and testing a variety of metamodels (linear regression, Gaussian processes, random forest, gradient boosting, etc.). Results reinforce the idea that for sufficiently statistically-converged quantities of interest and for a sufficiently large LES data set, a compound surrogate model can succeed in synthesizing information from the LES in the whole computational domain (with a Q 2 predictivity coefficient above 90 %). Downstream of the obstacle, the Q 2 coefficient of all metamodels reaches excellent results over 90%. Upstream, the tracer concentration is subject to strong discontinuities; combining metamodels allows to guarantee a good predictivity coefficient over 75%.

International audience; In atmospheric dispersion problems, mapping pollutant concentrations within the first tens or hundreds of meters from the emission point source still remains a modelling challenge. Computational fluid dynamics (CFD) approaches provide relevant insights into turbulent flow and pollutant concentration patterns in complex terrain such as urban and mountainous areas. At the forefront of CFD approaches, large-eddy simulations (LES) are a promising way to represent time and space variability of turbulent atmospheric flows and to assess public short-term exposures. LES are subject to uncertainties due to the intrinsic variability of environmental factors, among whom the large-scale meteorological forcing and the emission source characteristics.

Recent works have explored the potential of machine learning as data-driven turbulence closures for RANS and LES techniques. Beyond these advances, the high expressivity and agility of physics-informed neural networks (PINNs) make them promising candidates for full fluid flow PDE modeling. An important question is whether this new paradigm, exempt from the traditional notion of discretization of the underlying operators very much connected to the flow scales resolution, is capable of sustaining high levels of turbulence characterized by multi-scale features? We investigate the use of PINNs surrogate modeling for turbulent Rayleigh-Bénard (RB) convection flows in rough and smooth rectangular cavities, mainly relying on DNS temperature data from the fluid bulk. We carefully quantify the computational requirements under which the formulation is capable of accurately recovering the flow hidden quantities. We then propose a new padding technique to distribute some of the scattered coordinates-at which PDE residuals are minimized-around the region of labeled data acquisition. We show how it comes to play as a regularization close to the training boundaries which are zones of poor accuracy for standard PINNs and results in a noticeable global accuracy improvement at iso-budget. Finally, we propose for the first time to relax the incompressibility condition in such a way that it drastically benefits the optimization search and results in a much improved convergence of the composite loss function. The RB results obtained at high Rayleigh number Ra = 2 • 10 9 are particularly impressive: the predictive accuracy of the surrogate over the entire half a billion DNS coordinates yields errors for all flow variables ranging between [0.3% − 4%] in the relative L 2 norm, with a training relying only on 1.6% of the DNS data points.

International audience; Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. As these models become more complex to predict thrombus formation dynamics high computational cost must be alleviated and inherent uncertainties must be assessed. Evaluating model uncertainties allows to increase the confidence in model predictions and identify avenues of improvement for both thrombosis modeling and anti-platelet therapies. In this work, an uncertainty quantification analysis of a multi-constituent thrombosis model is performed considering a common assay for platelet function (PFA-100®). The analysis is facilitated thanks to time-evolving polynomial chaos expansions used as a parametric surrogate for the full thrombosis model considering two quantities of interest; namely, thrombus volume and occlusion percentage. The surrogate is thoroughly validated and provides a straightforward access to a global sensitivity analysis via computation of Sobol' coefficients. Six out of fifteen parameters linked to thrombus consitution, vWF activity, and platelet adhesion dynamics were found to be most influential in the simulation variability considering only individual effects; while parameter interactions are highlighted when considering the total Sobol' indices. The influential parameters are related to thrombus constitution, vWF activity and platelet to platelet adhesion dynamics. The surrogate model allowed to predict realistic PFA-100® closure times of 300,000 virtual cases that followed the trends observed in clinical data. The current methodology could be used including common anti-platelet therapies to identify scenarios that preserve the hematological balance.

International audience; Patient-specific models in medicine offer an emerging technology for simulation ofdisease progression and clinical interventions. Such simulations have the potential tooffer clinical decision support, and to strengthen evidence-based medical decisions.In this paper, we present a framework for patient-specific simulation of mitral valvedisease, building on a clinical pathway we have developed based on data acquisitionfrom routine echocardiography [1]. The left ventricle (LV) endocardium is obtained bysegmentation of echocardiographic image data, from which a finite element model ofthe LV hemodynamics is reconstructed [1]. We extend the LV model with aparametrized model of the mitral valve (MV) opening, which we use to simulatemitral valve leakage, and valve stenosis through reduced function in the valveopening and closing. The effect of the simulated valve diseases on the ventricularhemodynamics is analysed, and compared to real patient data for valve disease. TheLV model is implemented in FEniCS-HPC [2], an open source finite element methodframework targeting coupled multi-physics problems, and high performancecomputing platforms. The sensitivity of the simulation results with respect to the MVmodel is investigated, using uncertainty quantification techniques [3].

International audience; Variational data assimilation methods are well known and widely applied in geophysical domains toproblems affected by uncertainty of short- and long-term model predictions. The strength of this approach isto fuse available information in order to find a compromise between background model predictions andobservations where the associated weights are provided by error covariance matrices. A remarkabledifficulty in data assimilation is the lack of information for background error covariance modeling. In manyindustrial applications, due to the absence of historical observations/predictions, the background matrixmodelling remains empirical relying on some form of expertise and imposed physical constraints. This canbe problematic especially for short term prediction or static reconstruction when the ensemble methodsbecome inappropriate.

Hydrodynamics Abstract

Background: Aging-related arterial stiffness is associated with substantial changes in global and local arterial pressures. The subsequent early return of reflected pressure waves leads to an elevated left ventricular (LV) afterload and ultimately to a deleterious concentric LV remodeling. Purpose: To compute aortic time-resolved pressure fields of healthy subjects from 4D flow MRI and to define relevant pressure-based markers while investigating their relationship with age, LV remodeling, as well as tonometric augmentation index (AIx) and pulse wave velocity (PWV). Study Type: Retrospective. Population: Forty-seven healthy subjects (age: 49.5 ± 18 years, 24 women). Field Strength/Sequence: 3 T/4D flow MRI. Assessment: Spatiotemporal pressure fields were computed by integrating velocity-derived pressure gradients using Navier–Stokes equations, while assuming zero pressure at the sino-tubular junction. To quantify aortic pressure spatiotemporal variations, we defined the following markers: 1) volumetric aortic pressure propagation rates ΔPE1/ΔV and ΔPE2/ΔV, representing variations of early and late systolic relative pressure peaks along the aorta, respectively, according to the cumulated aortic volume; 2) ΔAPE1-PE2 defined in four aortic regions as the absolute difference between early and late systolic relative pressure peaks amplitude. Statistical Tests: Linear regression, Wilcoxon rank sum test, Bland–Altman analysis, and intraclass correlation coefficients (ICC). Results: Spatiotemporal variations of aortic pressure peaks were moderately to highly reproducible (ICC ≥0.50) and decreased significantly with age, in terms of absolute magnitude: ΔPE1/ΔV (r = 0.70, P < 0.005), ΔPE2/ΔV (r = –0.45, P < 0.005) and ΔAPE1-PE2 (|r| > 0.39, P < 0.005). ΔPE1/ΔV was associated with LV remodeling (r = 0.53, P < 0.001) and ascending aorta ΔAPE1-PE2 was associated with AIx (r = –0.59, P < 0.001). Both associations were independent of age and systolic blood pressures. Only weak associations were found between pressure indices and PWV (r ≤ 0.40). Data Conclusion: 4D flow MRI relative aortic pressures were consistent with physiological knowledge as demonstrated by their significant volumetric and temporal variations with age and their independent association with LV remodeling and augmentation index. Level of Evidence 2. Technical Efficacy Stage 3. J. Magn. Reson. Imaging 2019;50:982–993. Fil: Bouaou, Kevin. Université Pierre et Marie Curie; Francia Fil: Bargiotas, Ioannis. Université Paris-Saclay; Francia Fil: Dietenbeck, Thomas. Université Pierre et Marie Curie; Francia Fil: Bollache, Emilie. Université Pierre et Marie Curie; Francia Fil: Soulat, Gilles. Hopital Europeen Georges Pompidou; Francia Fil: Craiem, Damian. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Medicina Traslacional, Trasplante y Bioingeniería. Fundación Favaloro. Instituto de Medicina Traslacional, Trasplante y Bioingeniería; Argentina Fil: Houriez Gombaud Saintonge, Sophia. Université Pierre et Marie Curie; Francia Fil: De Cesare, Alain. Université Pierre et Marie Curie; Francia Fil: Gencer, Umit. Hopital Europeen Georges Pompidou; Francia Fil: Giron, Alain. Université Pierre et Marie Curie; Francia Fil: Redheuil, Alban. Université Pierre et Marie Curie; Francia Fil: Messas, Emmanuel. Hopital Europeen Georges Pompidou; Francia Fil: Lucor, Didier. Université Paris-Saclay; Francia Fil: Mousseaux, Elie. Hopital Europeen Georges Pompidou; Francia Fil: Kachenoura, Nadjia. Université Pierre et Marie Curie; Francia

International audience; An enhanced goal-oriented mesh adaptation method is presented based on aerodynamic functional total derivatives with respect to mesh nodes in a Reynolds-Averaged Navier-Stokes (RANS) finite-volume mono-block and non-matching multi-block-structured grid framework. This method falls under the category of methods involving the adjoint vector of the function of interest. The contribution of a Spalart–Allmaras turbulence model is taken into account through its linearization. Meshes are adapted accordingly to the proposed indicator. Applications to 2D RANS flow about a RAE2822 airfoil in transonic, and detached subsonic conditions are presented for the drag coefficient estimation. The asset of the proposed method is patent. The obtained 2D anisotropic mono-block mesh well captures flow features as well as global aerodynamic functionals. Interestingly, the constraints imposed by structured grids may be relaxed by the use of non-matching multi-block approach that limits the outward propagation of local mesh refinement through all of the computational domain. The proposed method also leads to accurate results for these multi-block meshes but at a fraction of the cost. Finally, the method is also successfully applied to a more complex geometry, namely, a mono-block mesh in a 3D RANS transonic flow about an M6 wing.; Une méthode d'adaptation de maillage ciblée est présentée. Elle est basée sur la dérivée totale des fonctions aérodynamiques par rapport aux coordonnées de maillage pour les équations Navier-Stokes (RANS) dans le contexte de simulations aérodynamiques volumes-finis avec des grilles mono-bloc ou multi-blocs non-coïncidentes. Cette méthode entre dans la catégorie des méthodes basées sur le vecteur adjoint discret. La contribution du modèle de turbulence de Spalart–Allmaras est prise en compte dans la linéarisation. Les maillages sont adaptés selon l'indicateur proposé. Une application à deux écoulements bi-dimensionnels autour du profil RAE2822 (condition transsonique et condition subsonique avec détachement) avec calcul de la traînée est présentée. L'efficacité de la méthode est bien démontrée sur ce cas. Le maillage mono-bloc anisotrope résultant de l'adaptation capture les zones critiques de l'écoulement et calcule bien la fonction aérodynamique d'intérêt. La contrainte de maillage liée au caractère structuré des grilles est relâchée grâce à des maillages multi-blocs non-coïncidents qui limitent la propagation des zones raffinées vers la frontière infini. La méthode proposée permet de nouveau d'obtenir des estimations de fonctions précises pour une fraction stricte du coût d'un raffinement global. Finalement, la méthode est aussi appliquée avec succès à un écoulement transsonique autour de l'aile ONERA M6..

International audience

International audience; no abstract