14 research outputs found
: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications
Digital twins have emerged as a key technology for optimizing the performance
of engineering products and systems. High-fidelity numerical simulations
constitute the backbone of engineering design, providing an accurate insight
into the performance of complex systems. However, large-scale, dynamic,
non-linear models require significant computational resources and are
prohibitive for real-time digital twin applications. To this end, reduced order
models (ROMs) are employed, to approximate the high-fidelity solutions while
accurately capturing the dominant aspects of the physical behavior. The present
work proposes a new machine learning (ML) platform for the development of ROMs,
to handle large-scale numerical problems dealing with transient nonlinear
partial differential equations. Our framework, mentioned as
, utilizes a singular value
decomposition (SVD) update methodology, to compute a linear subspace of the
multi-fidelity solutions during the simulation process,
convolutional autoencoders for nonlinear dimensionality reduction,
feed-forward neural networks to map the input parameters to
the latent spaces, and long short-term memory networks to
predict and forecast the dynamics of parametric solutions. The efficiency of
the framework is demonstrated for a 2D linear
convection-diffusion equation, the problem of fluid around a cylinder, and the
3D blood flow inside an arterial segment. The accuracy of the reconstructed
results demonstrates the robustness and assesses the efficiency of the proposed
approach.Comment: 35 pages, 22 figure
A voxelized immersed boundary (VIB) finite element method for accurate and efficient blood flow simulation
We present an efficient and accurate immersed boundary (IB) finite element
(FE) method for internal flow problems with complex geometries (e.g., blood
flow in the vascular system). In this study, we use a voxelized flow domain
(discretized with hexahedral and tetrahedral elements) instead of a box domain,
which is frequently used in IB methods. The proposed method utilizes the
well-established incremental pressure correction scheme (IPCS) FE solver, and
the boundary condition-enforced IB (BCE-IB) method to numerically solve the
transient, incompressible Navier--Stokes flow equations. We verify the accuracy
of our numerical method using the analytical solution for the Poiseuille flow
in a cylinder, and the available experimental data (laser Doppler velocimetry)
for the flow in a three-dimensional 90{\deg} angle tube bend. We further
examine the accuracy and applicability of the proposed method by considering
flow within complex geometries, such as blood flow in aneurysmal vessels and
the aorta, flow configurations that would otherwise be difficult to solve by
most IB methods. Our method offers high accuracy, as demonstrated by the
verification examples, and high applicability, as demonstrated through the
solution of blood flow within complex geometry. The proposed method is
efficient, since it is as fast as the traditional finite element method used to
solve the Navier--Stokes flow equations, with a small overhead (not more than
5) due to the numerical solution of a linear system formulated for the IB
method.Comment: arXiv admin note: substantial text overlap with arXiv:2007.0208
Characterization, Reconstruction and Transport Properties of Vosges Sandstones Caractérisation, reconstruction et propriétés de transport des grès des Vosges
A thorough study of Vosges sandstone samples is presented in this work. First, the geometry of these porous media is analyzed using serial thin sections. Then, random numerical samples are reconstructed according to the measured statistical geometrical parameters. Finally, the macroscopic transport properties are determined from the numerical solutions in the reconstructed samples of the local equations governing the corresponding transport phenomena and compared to available experimental data. Mercury intrusion in the simulated media is modelled and pore size distribution results are compared with those obtained from serial tomography. Dans cet article, nous présentons une étude approfondie d'échantillons de grès des Vosges. La géométrie de ces milieux est analysée en utilisant des coupes sériées. Puis des échantillons aléatoires sont reconstruits en accord avec les propriétés géométriques statistiques mesurées. Enfin, les propriétés macroscopiques de transport sont déduites des solutions numériques dans les échantillons reconstruits des équations locales qui régissent les transports correspondants, et elles sont comparées aux mesures disponibles. La pénétration de mercure dans les échantillons est modélisée et les résultats relatifs aux distributions de pores sont comparés à ceux obtenus sur les coupes sériées
Characterization, Reconstruction and Transport Properties of Vosges Sandstones
International audienceA thorough study of Vosges sandstone samples is presented in this work. First, the geometry of these porous media is analyzed using serial thin sections. Then, random numerical samples are reconstructed according to the measured statistical geometrical parameters. Finally, the macroscopic transport properties are determined from the numerical solutions in the reconstructed samples of the local equations governing the corresponding transport phenomena and compared to available experimental data. Mercury intrusion in the simulated media is modelled and pore size distribution results are compared with those obtained from serial tomography
Characterization, Reconstruction and Transport Properties of Vosges Sandstones
A thorough study of Vosges sandstone samples is presented in this work. First, the geometry of these porous media is analyzed using serial thin sections. Then, random numerical samples are reconstructed according to the measured statistical geometrical parameters. Finally, the macroscopic transport properties are determined from the numerical solutions in the reconstructed samples of the local equations governing the corresponding transport phenomena and compared to available experimental data. Mercury intrusion in the simulated media is modelled and pore size distribution results are compared with those obtained from serial tomography