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A posteriori error estimation for model order reduction of parametric systems Adv. Model. and Simul. in Eng. Sci. Pub Date : 2024-03-11 Lihong Feng, Sridhar Chellappa, Peter Benner
This survey discusses a posteriori error estimation for model order reduction of parametric systems, including linear and nonlinear, time-dependent and steady systems. We focus on introducing the error estimators we have proposed in the past few years and comparing them with the most related error estimators from the literature. For a clearer comparison, we have translated some existing error bounds
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The displacement mechanism of the cracked rock – a seismic design and prediction study using XFEM and ANNs Adv. Model. and Simul. in Eng. Sci. Pub Date : 2024-02-28 Omer Mughieda, Lijie Guo, Yunchao Tang, Nader M. Okasha, Sayed Javid Azimi, Abdoullah Namdar, Falak Azhar
Materials with sufficient strength and stiffness can transfer nonlinear design loads without damage. The present study compares crack propagation speed and shape in rock-like material and sandstone when subjected to seismic acceleration. The nonlinear extended finite element method (NXFEM) has been used in numerical simulation. It assumes the model has a pre-existing crack at 0° from the horizontal
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A hybrid twin based on machine learning enhanced reduced order model for real-time simulation of magnetic bearings Adv. Model. and Simul. in Eng. Sci. Pub Date : 2024-02-03 Chady Ghnatios, Sebastian Rodriguez, Jerome Tomezyk, Yves Dupuis, Joel Mouterde, Joaquim Da Silva, Francisco Chinesta
The simulation of magnetic bearings involves highly non-linear physics, with high dependency on the input variation. Moreover, such a simulation is time consuming and can’t run, within realistic computation time for control purposes, when using classical computation methods. On the other hand, classical model reduction techniques fail to achieve the required precision within the allowed computation
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Fast rapidly convergent penetrable scattering computations Adv. Model. and Simul. in Eng. Sci. Pub Date : 2024-01-20 Jagabandhu Paul, Ambuj Pandey, B. V. Rathish Kumar, Akash Anand
We present a fast high-order scheme for the numerical solution of a volume-surface integro-differential equation. Such equations arise in problems of scattering of time-harmonic acoustic and electromagnetic waves by inhomogeneous media with variable density wherein the material properties jump across the medium interface. The method uses a partition of unity to segregate the interior and the boundary
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Dimension independent data sets approximation and applications to classification Adv. Model. and Simul. in Eng. Sci. Pub Date : 2024-01-03 Patrick Guidotti
We revisit the classical kernel method of approximation/interpolation theory in a very specific context from the particular point of view of partial differential equations. The goal is to highlight the role of regularization by casting it in terms of actual smoothness of the interpolant obtained by the procedure. The latter will be merely continuous on the data set but smooth otherwise. While the method
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Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-11-30 Pratyush Bhatt, Yash Kumar, Azzeddine Soulaïmani
Physical systems whose dynamics are governed by partial differential equations (PDEs) find numerous applications in science and engineering. The process of obtaining the solution from such PDEs may be computationally expensive for large-scale and parameterized problems. In this work, deep learning techniques developed especially for time-series forecasts, such as LSTM and TCN, or for spatial-feature
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Real-world application of a discrete feedback control system for flexible biogas production Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-11-27 Lingga Aksara Putra, Bernhard Huber, Matthias Gaderer
Using renewable energy is increasingly prevalent as part of a global effort to safeguard the environment, with a reduction in $${\mathrm{CO}}_{2}$$ being one of the primary objectives. A biogas plant provides an opportunity to produce green energy, but its profitability prevents it from being utilized more frequently. A suitable response to this economic issue would be flexible biogas production to
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Classification and analysis of common simplifications in part-scale thermal modelling of metal additive manufacturing processes Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-11-08 Rajit Ranjan, Matthijs Langelaar, Fred Van Keulen, Can Ayas
Computational process modelling of metal additive manufacturing has gained significant research attention in recent past. The cornerstone of many process models is the transient thermal response during the AM process. Since deposition-scale modelling of the thermal conditions in AM is computationally expensive, spatial and temporal simplifications, such as simulating deposition of an entire layer or
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Solving multiphysics-based inverse problems with learned surrogates and constraints Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-10-11 Ziyi Yin, Rafael Orozco, Mathias Louboutin, Felix J. Herrmann
Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow
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On the flow conditions requiring detailed geometric modeling for multiscale evaluation of coastal forests Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-08-24 Reika Nomura, Shinsuke Takase, Shuji Moriguchi, Kenjiro Terada
The multiscale evaluation method is applied to assess the influence of detailed geometric modeling of trees on their macroscopic attenuation effect against tsunami-like flow. Specifically, we conduct a series of numerical flow tests (NFTs), i.e., 3D flow simulations in a local test domain (LTD), under various inflow conditions to evaluate the macroscopic flow characteristics in the LTD accommodating
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A DeepONet multi-fidelity approach for residual learning in reduced order modeling Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-07-26 Nicola Demo, Marco Tezzele, Gianluigi Rozza
In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the original model. The error introduced by the such operation is usually neglected and sacrificed in order to reach a fast computation. We propose to couple the model reduction
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Compatible interface wave–structure interaction model for combining mesh-free particle and finite element methods Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-07-26 Naoto Mitsume
This study presents a novel wave–structure interaction model, which is a compatible interface wave–structure interaction model that is based on mesh-free particle methods for free-surface flow analysis; the FEM for structural analysis. We adopt the explicitly represented polygon (ERP) wall boundary model, which is a polygon wall boundary model for mesh-free particle methods, to express the fluid–structure
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Scalable block preconditioners for saturated thermo-hydro-mechanics problems Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-06-26 Ana C. Ordonez, Nicolas Tardieu, Carola Kruse, Daniel Ruiz, Sylvie Granet
We are interested in the modelling of saturated thermo-hydro-mechanical (THM) problems that describe the behaviour of a soil in which a weakly compressible fluid evolves. It is used for the evaluation of the THM impact of high-level activity radioactive waste exothermicity within a deep geological disposal facility. We shall present the definition of a block preconditioner with nested Krylov solvers
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Sensitivity-guided iterative parameter identification and data generation with BayesFlow and PELS-VAE for model calibration Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-06-24 Yi Zhang, Lars Mikelsons
Calibration of complex system models with a large number of parameters using standard optimization methods is often extremely time-consuming and not fully automated due to the reliance on all-inclusive expert knowledge. We propose a sensitivity-guided iterative parameter identification and data generation algorithm. The sensitivity analysis replaces manual intervention, the parameter identification
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Numerical modelling of the process chain for aluminium Tailored Heat-Treated Profiles Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-06-12 Hannes Fröck, Matthias Graser, Michael Reich, Michael Lechner, Marion Merklein, Olaf Kessler
Lightweight construction in modern car design leads to an increased usage of various aluminium semi-finished products. Besides sheet material, aluminium extrusion profiles are frequently used due to their high stiffness and variety of possible cross-sections. However, similar to sheet material, aluminium profiles exhibit limited formability in comparison to mild steel materials. One possibility to
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Reduced-order modeling for stochastic large-scale and time-dependent flow problems using deep spatial and temporal convolutional autoencoders Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-05-19 Azzedine Abdedou, Azzeddine Soulaimani
A non-intrusive reduced-order model based on convolutional autoencoders is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatiotemporal large-scale flow problems. The objective is to perform accurate and rapid uncertainty analyses of the flow outputs of interest for which the input parameters are deemed uncertain. The data are constituted from a set
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Finite element method-enhanced neural network for forward and inverse problems Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-05-13 Rishith E. Meethal, Anoop Kodakkal, Mohamed Khalil, Aditya Ghantasala, Birgit Obst, Kai-Uwe Bletzinger, Roland Wüchner
We introduce a novel hybrid methodology that combines classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element methods and custom loss functions from neural networks are merged to form the algorithm. The Finite Element Method-enhanced Neural Network hybrid model (FEM-NN
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POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier–Stokes equations Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-03-18 Saddam Hijazi, Melina Freitag, Niels Landwehr
We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier–Stokes equations (NSE). In the proposed approach, the presence of simulated data for the fluid dynamics fields is assumed. A POD-Galerkin ROM is then constructed by applying POD on the snapshots matrices of the fluid fields and performing
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Regularized regressions for parametric models based on separated representations Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-03-09 Abel Sancarlos, Victor Champaney, Elias Cueto, Francisco Chinesta
Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding multi-parametric solutions can be viewed as a sort of computational vademecum that, once computed offline, can be then used in a variety of real-time engineering applications
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A “data-driven uncertainty” computational method to model and predict instabilities of a frictional system Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-02-13 Farouk Maaboudallah, Noureddine Atalla
Most of the recently developed methods for predicting instabilities of frictional systems couple stochastic algorithms with the finite element method (FEM). They use random variables to model the uncertainty of input parameters through standard probability laws. Regardless of the fact that advanced numerical schemes are available nowadays, a systematic and accurate method to describe finely the uncertainties
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Damage model for simulating cohesive fracture behavior of multi-phase composite materials Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-02-06 Mao Kurumatani, Takumi Kato, Hiromu Sasaki
We propose a new damage model for simulating the cohesive fracture behavior of multi-phase composite materials such as concrete. The proposed model can evaluate the damage of the matrix-phase in composite materials using the volume fraction of the matrix within an element comprising the matrix and other materials. The damage model was first formulated for 1D problems and then extended to two-dimensional
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Seepage failure prediction of breakwater using an unresolved ISPH-DEM coupling method enriched with Terzaghi’s critical hydraulic gradient Adv. Model. and Simul. in Eng. Sci. Pub Date : 2023-01-23 Kumpei Tsuji, Mitsuteru Asai, Kiyonobu Kasama
This study develops a new numerical simulation model for rubble mound failure prediction caused by piping destruction under seepage flows. The piping has been pointed out as a significant cause of breakwater failure during tsunamis. Once boiling and heaving occur on the mound surface, the piping suddenly propagates in the opposite direction of seepage flow. For the seepage failure prediction, a coupled
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Bayesian calibration of coupled computational mechanics models under uncertainty based on interface deformation Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-12-22 Willmann, Harald, Nitzler, Jonas, Brandstäter, Sebastian, Wall, Wolfgang A.
Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We present a Bayesian calibration approach for surface coupled problems in computational mechanics based on measured deformation of an interface when no displacement
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Multivariate moment-matching for model order reduction of quadratic-bilinear systems using error bounds Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-12-12 Khattak, Muhammad Altaf, Ahmad, Mian Ilyas, Feng, Lihong, Benner, Peter
We propose an adaptive moment-matching framework for model order reduction of quadratic-bilinear systems. In this framework, an important issue is the selection of those shift frequencies where moment-matching is to be achieved. So far, the choice often has been random or linked to the linear part of the nonlinear system. In this paper, we extend the use of an existing a posteriori error bound for
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The Pseudo-Direct Numerical Simulation Method considered as a Reduced Order Model Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-10-28 Idelsohn, Sergio R., Gimenez, Juan M., Nigro, Norberto M.
The multiscale method called Pseudo-Direct Numerical Simulation (P-DNS) is presented as a Reduced Order Model (ROM) aiming to solve problems obtaining similar accuracy to a solution with many degrees of freedom (DOF). The theoretical basis of P-DNS is other than any standard ROM. However, from a methodological point of view, P-DNS shares the idea of an offline computation, as ROM does, providing the
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Empowering engineering with data, machine learning and artificial intelligence: a short introductive review Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-10-27 Chinesta, Francisco, Cueto, Elias
Simulation-based engineering has been a major protagonist of the technology of the last century. However, models based on well established physics fail sometimes to describe the observed reality. They often exhibit noticeable differences between physics-based model predictions and measurements. This difference is due to several reasons: practical (uncertainty and variability of the parameters involved
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A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-09-30 Baek, Jonghyuk, Schlinkman, Ryan T., Beckwith, Frank N., Chen, Jiun-Shyan
The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challenging phenomena such as severe material deformation and fragmentation. In contrast, meshfree methods such as the reproducing kernel particle method (RKPM) possess unique features conducive to
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A multi-point constraint unfitted finite element method Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-09-21 Freeman, Brubeck Lee
In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical
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Thermo-mechanical simulations of powder bed fusion processes: accuracy and efficiency Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-09-12 Burkhardt, Christian, Steinmann, Paul, Mergheim, Julia
In this contribution, the accuracy and efficiency of various modeling assumptions and numerical settings in thermo-mechanical simulations of powder bed fusion (PBF) processes are analyzed. Thermo-mechanical simulations are used to develop a better understanding of the process and to determine residual stresses and distortions based on the temperature history. In these numerically very complex simulations
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Stress-constrained topology optimization using approximate reanalysis with on-the-fly reduced order modeling Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-09-06 Xiao, Manyu, Ma, Jun, Lu, Dongcheng, Raghavan, Balaji, Zhang, Weihong
Most of the methods used today for handling local stress constraints in topology optimization, fail to directly address the non-self-adjointness of the stress-constrained topology optimization problem. This in turn could drastically raise the computational cost for an already large-scale problem. These problems involve both the equilibrium equations resulting from finite element analysis (FEA) in each
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A partitioned material point method and discrete element method coupling scheme Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-08-16 Singer, Veronika, Sautter, Klaus B., Larese, Antonia, Wüchner, Roland, Bletzinger, Kai-Uwe
Mass-movement hazards involving fast and large soil deformation often include huge rocks or other significant obstacles increasing tremendously the risks for humans and infrastructures. Therefore, numerical investigations of such disasters are in high economic demand for prediction as well as for the design of countermeasures. Unfortunately, classical numerical approaches are not suitable for such
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A Lagrangian–Eulerian procedure for the coupled solution of the Navier–Stokes and shallow water equations for landslide-generated waves Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-07-30 Masó, Miguel, Franci, Alessandro, de-Pouplana, Ignasi, Cornejo, Alejandro, Oñate, Eugenio
This work presents a partitioned method for landslide-generated wave events. The proposed strategy combines a Lagrangian Navier Stokes multi-fluid solver with an Eulerian method based on the Boussinesq shallow water equations. The Lagrangian solver uses the Particle Finite Element Method to model the landslide runout, its impact against the water body and the consequent wave generation. The results
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Numerical modeling of the propagation process of landslide surge using physics-informed deep learning Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-07-12 Wu, Yinghan, Shao, Kaixuan, Piccialli, Francesco, Mei, Gang
The landslide surge is a common secondary disaster of reservoir bank landslides, which can cause more serious damage than the landslide itself in many cases. With the development of large-scale scientific and engineering computing, many new techniques have been applied to the study of hydrodynamic problems to make up for the shortcomings of traditional methods. In this paper, we use the physics-informed
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A physics-based neural network for flight dynamics modelling and simulation Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-07-04 Stachiw, Terrin, Crain, Alexander, Ricciardi, Joseph
The authors have developed a novel physics-based nonlinear autoregressive exogeneous neural network model architecture for flight modelling across the entire flight envelope, called FlyNet. When using traditional parameter estimation and output-error methods, aircraft models are captured about a single point in the flight envelope using a first-order Taylor series to approximate forces and moments
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An energy-based study of the embedded element method for explicit dynamics Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-07-02 Martin, Valerie A., Kraft, Reuben H., Hannah, Thomas H., Ellis, Stephen
The embedded finite element technique provides a unique approach for modeling of fiber-reinforced composites. Meshing fibers as distinct bundles represented by truss elements embedded in a matrix material mesh allows for the assignment of more specific material properties for each component rather than homogenization of all of the properties. However, the implementations of the embedded element technique
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A methodology to assess and improve the physics consistency of an artificial neural network regression model for engineering applications Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-07-02 Rajasekhar Nicodemus, E.
In recent times, artificial neural networks (ANNs) have become the popular choice of model for researchers while performing regression analysis between inputs and output. However; in scientific and engineering applications, developed ANN regression model is often found to be inconsistent with the physical laws. This is due to the fact that ANNs are purely based on data and do not have any understanding
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Physics-Informed Neural Network water surface predictability for 1D steady-state open channel cases with different flow types and complex bed profile shapes Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-06-30 Cedillo, Sebastián, Núñez, Ana-Gabriela, Sánchez-Cordero, Esteban, Timbe, Luis, Samaniego, Esteban, Alvarado, Andrés
The behavior of many physical systems is described by means of differential equations. These equations are usually derived from balance principles and certain modelling assumptions. For realistic situations, the solution of the associated initial boundary value problems requires the use of some discretization technique, such as finite differences or finite volumes. This research tackles the numerical
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One-way coupled fluid–beam interaction: capturing the effect of embedded slender bodies on global fluid flow and vice versa Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-06-21 Hagmeyer, Nora, Mayr, Matthias, Steinbrecher, Ivo, Popp, Alexander
This work addresses research questions arising from the application of geometrically exact beam theory in the context of fluid-structure interaction (FSI). Geometrically exact beam theory has proven to be a computationally efficient way to model the behavior of slender structures while leading to rather well-posed problem descriptions. In particular, we propose a mixed-dimensional embedded finite element
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Geometry aware physics informed neural network surrogate for solving Navier–Stokes equation (GAPINN) Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-06-21 Oldenburg, Jan, Borowski, Finja, Öner, Alper, Schmitz, Klaus-Peter, Stiehm, Michael
Many real world problems involve fluid flow phenomena, typically be described by the Navier–Stokes equations. The Navier–Stokes equations are partial differential equations (PDEs) with highly nonlinear properties. Currently mostly used methods solve this differential equation by discretizing geometries. In the field of fluid mechanics the finite volume method (FVM) is widely used for numerical flow
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Inverse analysis of material parameters in coupled multi-physics biofilm models Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-06-15 Willmann, Harald, Wall, Wolfgang A.
In this article we propose an inverse analysis algorithm to find the best fit of multiple material parameters in different coupled multi-physics biofilm models. We use a nonlinear continuum mechanical approach to model biofilm deformation that occurs in flow cell experiments. The objective function is based on a simple geometrical measurement of the distance of the fluid biofilm interface between model
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A comparison of mixed-variables Bayesian optimization approaches Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-06-09 Cuesta Ramirez, Jhouben, Le Riche, Rodolphe, Roustant, Olivier, Perrin, Guillaume, Durantin, Cédric, Glière, Alain
Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation. General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific
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Physics-informed neural networks approach for 1D and 2D Gray-Scott systems Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-05-25 Giampaolo, Fabio, De Rosa, Mariapia, Qi, Pian, Izzo, Stefano, Cuomo, Salvatore
Nowadays, in the Scientific Machine Learning (SML) research field, the traditional machine learning (ML) tools and scientific computing approaches are fruitfully intersected for solving problems modelled by Partial Differential Equations (PDEs) in science and engineering applications. Challenging SML methodologies are the new computational paradigms named Physics-Informed Neural Networks (PINNs). PINN
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Spline-based specimen shape optimization for robust material model calibration Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-05-16 Chapelier, Morgane, Bouclier, Robin, Passieux, Jean-Charles
Identification from field measurements allows several parameters to be identified from a single test, provided that the measurements are sensitive enough to the parameters to be identified. To do this, authors use empirically defined geometries (with holes, notches...). The first attempts to optimize the specimen to maximize the sensitivity of the measurement are linked to a design space that is either
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An updated Gappy-POD to capture non-parameterized geometrical variation in fluid dynamics problems Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-03-11 Akkari, Nissrine, Casenave, Fabien, Ryckelynck, David, Rey, Christian
In this work, we propose a new method to fill the gap within an incomplete turbulent and incompressible data field in such a way to satisfy the topological and intensity changes of the fluid flow after a non-parameterized geometrical variation in the fluid domain. This work extends the one that has been published as a conference proceeding to the 2018 AIAA Scitech Forum and Exposition (Akkari et al
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Domain decomposition involving subdomain separable space representations for solving parametric problems in complex geometries Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-03-07 Kazemzadeh-Parsi, Mohammad Javad, Ammar, Amine, Chinesta, Francisco
A domain decomposition technique combined with an enhanced geometry mapping based on the use of NURBS is considered for solving parametrized models in complex geometries (non simply connected) within the so-called proper generalized decomposition (PGD) framework, enabling the expression of the solution in each subdomain in a fully separated form, involving both the space and the model parameters. NURBS
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Metamodeling techniques for CPU-intensive simulation-based design optimization: a survey Adv. Model. and Simul. in Eng. Sci. Pub Date : 2022-02-18 Khatouri, Hanane, Benamara, Tariq, Breitkopf, Piotr, Demange, Jean
In design optimization of complex systems, the surrogate model approach relying on progressively enriched Design of Experiments (DOE) avoids efficiency problems encountered when embedding simulation codes within optimization loops. However, an efficient a priori sampling of the design space rapidly becomes costly when using High-Fidelity (HF) simulators, especially in high dimension. On the other hand
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Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-12-30 Bai, Zhe, Peng, Liqian
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally
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Computational method for solving weakly singular Fredholm integral equations of the second kind using an advanced barycentric Lagrange interpolation formula Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-12-08 Shoukralla, E. S., Saber, Nermin, Sayed, Ahmed Y.
In this study, we applied an advanced barycentric Lagrange interpolation formula to find the interpolate solutions of weakly singular Fredholm integral equations of the second kind. The kernel is interpolated twice concerning both variables and then is transformed into the product of five matrices; two of them are monomial basis matrices. To isolate the singularity of the kernel, we developed two techniques
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A separated representation involving multiple time scales within the Proper Generalized Decomposition framework Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-11-26 Pasquale, Angelo, Ammar, Amine, Falcó, Antonio, Perotto, Simona, Cueto, Elías, Duval, Jean-Louis, Chinesta, Francisco
Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated
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Evaluation of POD based surrogate models of fields resulting from nonlinear FEM simulations Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-11-03 de Gooijer, Boukje M., Havinga, Jos, Geijselaers, Hubert J. M., van den Boogaard, Anton H.
Surrogate modelling is a powerful tool to replace computationally expensive nonlinear numerical simulations, with fast representations thereof, for inverse analysis, model-based control or optimization. For some problems, it is required that the surrogate model describes a complete output field. To construct such surrogate models, proper orthogonal decomposition (POD) can be used to reduce the dimensionality
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A simple yet consistent constitutive law and mortar-based layer coupling schemes for thermomechanical macroscale simulations of metal additive manufacturing processes Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-10-19 Proell, Sebastian D., Wall, Wolfgang A., Meier, Christoph
This article proposes a coupled thermomechanical finite element model tailored to the macroscale simulation of metal additive manufacturing processes such as selective laser melting. A first focus lies on the derivation of a consistent constitutive law on basis of a Voigt-type spatial homogenization procedure across the relevant phases, powder, melt and solid. The proposed constitutive law accounts
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Enhanced parametric shape descriptions in PGD-based space separated representations Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-10-04 Kazemzadeh-Parsi, Mohammad Javad, Ammar, Amine, Duval, Jean Louis, Chinesta, Francisco
Space separation within the Proper Generalized Decomposition—PGD—rationale allows solving high dimensional problems as a sequence of lower dimensional ones. In our former works, different geometrical transformations were proposed for addressing complex shapes and spatially non-separable domains. Efficient implementation of separated representations needs expressing the domain as a product of characteristic
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Industrial Digital Twins based on the non-linear LATIN-PGD Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-10-04 Barabinot, Philippe, Scanff, Ronan, Ladevèze, Pierre, Néron, David, Cauville, Bruno
Digital Twins, which tend to intervene over the entire life cycle of products from early design phase to predictive maintenance through optimization processes, are increasingly emerging as an essential component in the future of industries. To reduce the computational time reduced-order modeling (ROM) methods can be useful. However, the spread of ROM methods at an industrial level is currently hampered
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Coupling reduced-order blood flow and cardiac models through energy-consistent strategies: modeling and discretization Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-09-28 Manganotti, Jessica, Caforio, Federica, Kimmig, François, Moireau, Philippe, Imperiale, Sebastien
In this work we provide a novel energy-consistent formulation for the classical 1D formulation of blood flow in an arterial segment. The resulting reformulation is shown to be suitable for the coupling with a lumped (0D) model of the heart that incorporates a reduced formulation of the actin-myosin interaction. The coupling being consistent with energy balances, we provide a complete heart-circulation
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A nonparametric probabilistic method to enhance PGD solutions with data-driven approach, application to the automated tape placement process Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-09-21 Ghnatios, Chady, Barasinski, Anais
A nonparametric method assessing the error and variability margins in solutions depicted in a separated form using experimental results is illustrated in this work. The method assess the total variability of the solution including the modeling error and the truncation error when experimental results are available. The illustrated method is based on the use of the PGD separated form solutions, enriched
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Investigation of pollutants formation in a diesel engine using numerical simulation Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-09-04 Zahid, Muhammad, Syed, Khalid S.
The current study aims at simulating the in-cylinder combustion process in a diesel engine and investigating the engine performance and pollutant formation. The combustion simulation is performed on a 3D sector employing appropriate models for various physical and chemical processes contributing in the combustion phenomenon. The overall model includes Transition SST turbulence model, eddy dissipation
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Greedy maximin distance sampling based model order reduction of prestressed and parametrized abdominal aortic aneurysms Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-09-04 Schein, Alexander, Gee, Michael W.
This work proposes a framework for projection-based model order reduction (MOR) of computational models aiming at a mechanical analysis of abdominal aortic aneurysms (AAAs). The underlying full-order model (FOM) is patient-specific, stationary and nonlinear. The quantities of interest are the von Mises stress and the von Mises strain field in the AAA wall, which result from loading the structure to
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A generalized Fourier transform by means of change of variables within multilinear approximation Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-08-04 Chevreuil, Mathilde, Slama, Myriam
The paper deals with approximations of periodic functions that play a significant role in harmonic analysis. The approach revisits the trigonometric polynomials, seen as combinations of functions, and proposes to extend the class of models of the combined functions to a wider class of functions. The key here is to use structured functions, that have low complexity, with suitable functional representation
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A novel physics-based and data-supported microstructure model for part-scale simulation of laser powder bed fusion of Ti-6Al-4V Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-07-27 Nitzler, Jonas, Meier, Christoph, Müller, Kei W., Wall, Wolfgang A., Hodge, N. E.
The elasto-plastic material behavior, material strength and failure modes of metals fabricated by additive manufacturing technologies are significantly determined by the underlying process-specific microstructure evolution. In this work a novel physics-based and data-supported phenomenological microstructure model for Ti-6Al-4V is proposed that is suitable for the part-scale simulation of laser powder
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An SPH framework for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions Adv. Model. and Simul. in Eng. Sci. Pub Date : 2021-06-28 Sebastian L. Fuchs, Christoph Meier, Wolfgang A. Wall, Christian J. Cyron
The present work proposes an approach for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable but mobile rigid bodies, that are evolved in time individually and allowed to get into mechanical contact with each other. The fluid field generally consists of