Pub Date : 2024-09-16DOI: 10.1186/s40323-024-00272-4
Ginevra Covoni, Francesco Montomoli, Vito L. Tagarielli, Valentina Bisio, Stefano Rossin, Marco Ruggiero
We illustrate an application of graph neural networks (GNNs) to predict the pressure, temperature and velocity fields induced by a sudden explosion. The aim of the work is to enable accurate simulation of explosion events in large and geometrically complex domains. Such simulations are currently out of the reach of existing CFD solvers, which represents an opportunity to apply machine learning. The training dataset is obtained from the results of URANS analyses in OpenFOAM. We simulate the transient flow following impulsive events in air in atmospheric conditions. The time history of the fields of pressure, temperature and velocity obtained from a set of such simulations is then recorded to serve as a training database. In the training simulations we model a cubic volume of air enclosed within rigid walls, which also encompass rigid obstacles of random shape, position and orientation. A subset of the cubic volume is initialized to have a higher pressure than the rest of the domain. The ensuing shock initiates the propagation of pressure waves and their reflection and diffraction at the obstacles and walls. A recently proposed GNN framework is extended and adapted to this problem. During the training, the model learns the evolution of thermodynamic quantities in time and space, as well as the effect of the boundary conditions. After training, the model can quickly compute such evolution for unseen geometries and arbitrary initial and boundary conditions, exhibiting good generalization capabilities for domains up to 125 times larger than those used in the training simulations.
{"title":"Application of graph neural networks to predict explosion-induced transient flow","authors":"Ginevra Covoni, Francesco Montomoli, Vito L. Tagarielli, Valentina Bisio, Stefano Rossin, Marco Ruggiero","doi":"10.1186/s40323-024-00272-4","DOIUrl":"https://doi.org/10.1186/s40323-024-00272-4","url":null,"abstract":"We illustrate an application of graph neural networks (GNNs) to predict the pressure, temperature and velocity fields induced by a sudden explosion. The aim of the work is to enable accurate simulation of explosion events in large and geometrically complex domains. Such simulations are currently out of the reach of existing CFD solvers, which represents an opportunity to apply machine learning. The training dataset is obtained from the results of URANS analyses in OpenFOAM. We simulate the transient flow following impulsive events in air in atmospheric conditions. The time history of the fields of pressure, temperature and velocity obtained from a set of such simulations is then recorded to serve as a training database. In the training simulations we model a cubic volume of air enclosed within rigid walls, which also encompass rigid obstacles of random shape, position and orientation. A subset of the cubic volume is initialized to have a higher pressure than the rest of the domain. The ensuing shock initiates the propagation of pressure waves and their reflection and diffraction at the obstacles and walls. A recently proposed GNN framework is extended and adapted to this problem. During the training, the model learns the evolution of thermodynamic quantities in time and space, as well as the effect of the boundary conditions. After training, the model can quickly compute such evolution for unseen geometries and arbitrary initial and boundary conditions, exhibiting good generalization capabilities for domains up to 125 times larger than those used in the training simulations.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142257159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-27DOI: 10.1186/s40323-024-00271-5
Salma Jahan, Rehena Nasrin
Microchannel heat exchangers have become the preferred choice in contemporary technologies like electronics, refrigeration, and thermal management systems. Their popularity stems from their compact design and exceptional efficiency, which outperform traditional heat exchangers (HE). Despite ongoing efforts, the optimal microchannels for enhancing heat management, minimizing pressure drop, and boosting overall performance have yet to be identified. This study seeks to deepen our understanding of heat transmission and fluid dynamics within a cross-flow microchannel heat exchanger (CFMCHE). Utilizing numerical modeling, it examines how various physical aspects—such as channel geometry, spacing between channels, the number of channels, and the velocity at the inlet—affect key performance indicators like pressure drop, effectiveness, Nusselt number, and overall efficiency. To enhance the design, we analyze six unique shapes of crossflow microchannel heat exchangers: circular, hexagonal, trapezoidal, square, triangular, and rectangular. We employ the Galerkin-developed weighted residual finite element method to numerically address the governing three-dimensional conjugate partial differential coupled equations. The numerical results for each shape are presented, focusing on the surface temperature, pressure drop, and temperature contours. Additionally, calculations include the efficacy, the heat transfer rate in relation to pumping power, and the overall performance index. The findings reveal that while circular shapes achieve the highest heat transfer rates, they underperform compared to square-shaped CFMCHEs. This underperformance is largely due to the increased pressure drop in circular channels, which also exhibit a 1.03% greater reduction in effectiveness rate than their square-shaped counterparts. Consequently, square-shaped channels, boasting a performance index growth rate of 53.57%, emerge as the most effective design among the six shapes evaluated. Additionally, for the square-shaped CFMCHE, we include residual error plots and present a multiple-variable linear regression equation that boasts a correlation coefficient of 0.8026.
{"title":"Role of physical structure on performance index of crossflow microchannel heat exchanger with regression analysis","authors":"Salma Jahan, Rehena Nasrin","doi":"10.1186/s40323-024-00271-5","DOIUrl":"https://doi.org/10.1186/s40323-024-00271-5","url":null,"abstract":"Microchannel heat exchangers have become the preferred choice in contemporary technologies like electronics, refrigeration, and thermal management systems. Their popularity stems from their compact design and exceptional efficiency, which outperform traditional heat exchangers (HE). Despite ongoing efforts, the optimal microchannels for enhancing heat management, minimizing pressure drop, and boosting overall performance have yet to be identified. This study seeks to deepen our understanding of heat transmission and fluid dynamics within a cross-flow microchannel heat exchanger (CFMCHE). Utilizing numerical modeling, it examines how various physical aspects—such as channel geometry, spacing between channels, the number of channels, and the velocity at the inlet—affect key performance indicators like pressure drop, effectiveness, Nusselt number, and overall efficiency. To enhance the design, we analyze six unique shapes of crossflow microchannel heat exchangers: circular, hexagonal, trapezoidal, square, triangular, and rectangular. We employ the Galerkin-developed weighted residual finite element method to numerically address the governing three-dimensional conjugate partial differential coupled equations. The numerical results for each shape are presented, focusing on the surface temperature, pressure drop, and temperature contours. Additionally, calculations include the efficacy, the heat transfer rate in relation to pumping power, and the overall performance index. The findings reveal that while circular shapes achieve the highest heat transfer rates, they underperform compared to square-shaped CFMCHEs. This underperformance is largely due to the increased pressure drop in circular channels, which also exhibit a 1.03% greater reduction in effectiveness rate than their square-shaped counterparts. Consequently, square-shaped channels, boasting a performance index growth rate of 53.57%, emerge as the most effective design among the six shapes evaluated. Additionally, for the square-shaped CFMCHE, we include residual error plots and present a multiple-variable linear regression equation that boasts a correlation coefficient of 0.8026.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-29DOI: 10.1186/s40323-024-00268-0
Thomas Schneider, Alexandre Beiderwellen Bedrikow, Karsten Stahl
This research paper presents a comprehensive methodology for analyzing wet clutches, focusing on their intricate thermomechanical behavior. The study combines advanced encoding techniques, such as Principal Component Analysis (PCA), with metamodeling, to efficiently predict pressure and temperature distributions on friction surfaces. By parametrically varying input parameters and utilizing Finite Element Method (FEM) simulations, we generate a dataset comprising 200 simulations, divided into training and testing sets. Our findings indicate that PCA encoding effectively reduces data dimensionality while preserving essential information. Notably, the study reveals that only a few PCA components are required for accurate encoding: two components for temperature distribution and pressure, and three components for heat flux density. We compare various metamodeling techniques, including Linear Regression, Decision Trees, Random Forest, Support Vector Regression, Gaussian Processes, and Neural Networks. The results underscore the varying performance of these techniques, with Random Forest excelling in mechanical metamodeling and Neural Networks demonstrating superiority in thermal metamodeling.
{"title":"Enhanced prediction of thermomechanical systems using machine learning, PCA, and finite element simulation","authors":"Thomas Schneider, Alexandre Beiderwellen Bedrikow, Karsten Stahl","doi":"10.1186/s40323-024-00268-0","DOIUrl":"https://doi.org/10.1186/s40323-024-00268-0","url":null,"abstract":"This research paper presents a comprehensive methodology for analyzing wet clutches, focusing on their intricate thermomechanical behavior. The study combines advanced encoding techniques, such as Principal Component Analysis (PCA), with metamodeling, to efficiently predict pressure and temperature distributions on friction surfaces. By parametrically varying input parameters and utilizing Finite Element Method (FEM) simulations, we generate a dataset comprising 200 simulations, divided into training and testing sets. Our findings indicate that PCA encoding effectively reduces data dimensionality while preserving essential information. Notably, the study reveals that only a few PCA components are required for accurate encoding: two components for temperature distribution and pressure, and three components for heat flux density. We compare various metamodeling techniques, including Linear Regression, Decision Trees, Random Forest, Support Vector Regression, Gaussian Processes, and Neural Networks. The results underscore the varying performance of these techniques, with Random Forest excelling in mechanical metamodeling and Neural Networks demonstrating superiority in thermal metamodeling.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-13DOI: 10.1186/s40323-024-00264-4
Tomas Vaitkunas, Paulius Griskevicius, Gintautas Dundulis, Stephan Courtin
Numerical fatigue process modelling is complex and still an open task. Discontinuity caused by fatigue cracks requires special finite element techniques based on additional parameters, the selection of which has a strong effect on the simulation results. Moreover, the calculation of fatigue life according to empirical material coefficients (e.g., Paris law) does not explain the process, and coefficients should be set from experimental testing, which is not always possible. A new nonlocal continuum mechanics formulation without spatial derivative of coordinates, namely, peridynamics (PD), which was created 20 y ago, provides new opportunities for modelling discontinuities, such as fatigue cracks. The fatigue process can be better described by using the atomistic approach-based kinetic theory of fracture (KTF), which includes the process temperature, maximum and minimum stresses, and loading frequency in its differential fatigue damage equation. Standard 316L stainless steel specimens are tested, and then the KTF-PD fatigue simulation is run in this study. In-house MATLAB code, calibrated from the material S‒N curve, is used for the KTF-PD simulation. A novel KTF equation based on the cycle stress‒strain hysteresis loop is proposed and applied to predict fatigue life. The simulation results are compared with the experimental results, and good agreement is observed for both symmetric and asymmetric cyclic loading.
{"title":"Peridynamic numerical investigation of asymmetric strain-controlled fatigue behaviour using the kinetic theory of fracture","authors":"Tomas Vaitkunas, Paulius Griskevicius, Gintautas Dundulis, Stephan Courtin","doi":"10.1186/s40323-024-00264-4","DOIUrl":"https://doi.org/10.1186/s40323-024-00264-4","url":null,"abstract":"Numerical fatigue process modelling is complex and still an open task. Discontinuity caused by fatigue cracks requires special finite element techniques based on additional parameters, the selection of which has a strong effect on the simulation results. Moreover, the calculation of fatigue life according to empirical material coefficients (e.g., Paris law) does not explain the process, and coefficients should be set from experimental testing, which is not always possible. A new nonlocal continuum mechanics formulation without spatial derivative of coordinates, namely, peridynamics (PD), which was created 20 y ago, provides new opportunities for modelling discontinuities, such as fatigue cracks. The fatigue process can be better described by using the atomistic approach-based kinetic theory of fracture (KTF), which includes the process temperature, maximum and minimum stresses, and loading frequency in its differential fatigue damage equation. Standard 316L stainless steel specimens are tested, and then the KTF-PD fatigue simulation is run in this study. In-house MATLAB code, calibrated from the material S‒N curve, is used for the KTF-PD simulation. A novel KTF equation based on the cycle stress‒strain hysteresis loop is proposed and applied to predict fatigue life. The simulation results are compared with the experimental results, and good agreement is observed for both symmetric and asymmetric cyclic loading.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-03DOI: 10.1186/s40323-024-00265-3
Tarik Sahin, Max von Danwitz, Alexander Popp
This paper explores the ability of physics-informed neural networks (PINNs) to solve forward and inverse problems of contact mechanics for small deformation elasticity. We deploy PINNs in a mixed-variable formulation enhanced by output transformation to enforce Dirichlet and Neumann boundary conditions as hard constraints. Inequality constraints of contact problems, namely Karush–Kuhn–Tucker (KKT) type conditions, are enforced as soft constraints by incorporating them into the loss function during network training. To formulate the loss function contribution of KKT constraints, existing approaches applied to elastoplasticity problems are investigated and we explore a nonlinear complementarity problem (NCP) function, namely Fischer–Burmeister, which possesses advantageous characteristics in terms of optimization. Based on the Hertzian contact problem, we show that PINNs can serve as pure partial differential equation (PDE) solver, as data-enhanced forward model, as inverse solver for parameter identification, and as fast-to-evaluate surrogate model. Furthermore, we demonstrate the importance of choosing proper hyperparameters, e.g. loss weights, and a combination of Adam and L-BFGS-B optimizers aiming for better results in terms of accuracy and training time.
{"title":"Solving forward and inverse problems of contact mechanics using physics-informed neural networks","authors":"Tarik Sahin, Max von Danwitz, Alexander Popp","doi":"10.1186/s40323-024-00265-3","DOIUrl":"https://doi.org/10.1186/s40323-024-00265-3","url":null,"abstract":"This paper explores the ability of physics-informed neural networks (PINNs) to solve forward and inverse problems of contact mechanics for small deformation elasticity. We deploy PINNs in a mixed-variable formulation enhanced by output transformation to enforce Dirichlet and Neumann boundary conditions as hard constraints. Inequality constraints of contact problems, namely Karush–Kuhn–Tucker (KKT) type conditions, are enforced as soft constraints by incorporating them into the loss function during network training. To formulate the loss function contribution of KKT constraints, existing approaches applied to elastoplasticity problems are investigated and we explore a nonlinear complementarity problem (NCP) function, namely Fischer–Burmeister, which possesses advantageous characteristics in terms of optimization. Based on the Hertzian contact problem, we show that PINNs can serve as pure partial differential equation (PDE) solver, as data-enhanced forward model, as inverse solver for parameter identification, and as fast-to-evaluate surrogate model. Furthermore, we demonstrate the importance of choosing proper hyperparameters, e.g. loss weights, and a combination of Adam and L-BFGS-B optimizers aiming for better results in terms of accuracy and training time.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"155 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-29DOI: 10.1186/s40323-024-00266-2
Chady Ghnatios, Daniele Di Lorenzo, Victor Champaney, Amine Ammar, Elias Cueto, Francisco Chinesta
Trajectory planning aims at computing an optimal trajectory through the minimization of a cost function. This paper considers four different scenarios: (i) the first concerns a given trajectory on which a cost function is minimized by a acting on the velocity along it; (ii) the second considers trajectories expressed parametrically, from which an optimal path and the velocity along it are computed; (iii), the case in which only the departure and arrival points of the trajectory are known, and the optimal path must be determined; and finally, (iv) the case involving uncertainty in the environment in which the trajectory operates. When the considered cost functions are expressed analytically, the application of Euler–Lagrange equations constitutes an appealing option. However, in many applications, complex cost functions are learned by using black-box machine learning techniques, for instance deep neural networks. In such cases, a neural approach of the trajectory planning becomes an appealing alternative. Different numerical experiments will serve to illustrate the potential of the proposed methodologies on some selected use cases.
{"title":"Optimal trajectory planning combining model-based and data-driven hybrid approaches","authors":"Chady Ghnatios, Daniele Di Lorenzo, Victor Champaney, Amine Ammar, Elias Cueto, Francisco Chinesta","doi":"10.1186/s40323-024-00266-2","DOIUrl":"https://doi.org/10.1186/s40323-024-00266-2","url":null,"abstract":"Trajectory planning aims at computing an optimal trajectory through the minimization of a cost function. This paper considers four different scenarios: (i) the first concerns a given trajectory on which a cost function is minimized by a acting on the velocity along it; (ii) the second considers trajectories expressed parametrically, from which an optimal path and the velocity along it are computed; (iii), the case in which only the departure and arrival points of the trajectory are known, and the optimal path must be determined; and finally, (iv) the case involving uncertainty in the environment in which the trajectory operates. When the considered cost functions are expressed analytically, the application of Euler–Lagrange equations constitutes an appealing option. However, in many applications, complex cost functions are learned by using black-box machine learning techniques, for instance deep neural networks. In such cases, a neural approach of the trajectory planning becomes an appealing alternative. Different numerical experiments will serve to illustrate the potential of the proposed methodologies on some selected use cases.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-18DOI: 10.1186/s40323-024-00263-5
Eki Agouzal, Tommaso Taddei
We present an accelerated greedy strategy for training of projection-based reduced-order models for parametric steady and unsteady partial differential equations. Our approach exploits hierarchical approximate proper orthogonal decomposition to speed up the construction of the empirical test space for least-square Petrov–Galerkin formulations, a progressive construction of the empirical quadrature rule based on a warm start of the non-negative least-square algorithm, and a two-fidelity sampling strategy to reduce the number of expensive greedy iterations. We illustrate the performance of our method for two test cases: a two-dimensional compressible inviscid flow past a LS89 blade at moderate Mach number, and a three-dimensional nonlinear mechanics problem to predict the long-time structural response of the standard section of a nuclear containment building under external loading.
{"title":"Accelerated construction of projection-based reduced-order models via incremental approaches","authors":"Eki Agouzal, Tommaso Taddei","doi":"10.1186/s40323-024-00263-5","DOIUrl":"https://doi.org/10.1186/s40323-024-00263-5","url":null,"abstract":"We present an accelerated greedy strategy for training of projection-based reduced-order models for parametric steady and unsteady partial differential equations. Our approach exploits hierarchical approximate proper orthogonal decomposition to speed up the construction of the empirical test space for least-square Petrov–Galerkin formulations, a progressive construction of the empirical quadrature rule based on a warm start of the non-negative least-square algorithm, and a two-fidelity sampling strategy to reduce the number of expensive greedy iterations. We illustrate the performance of our method for two test cases: a two-dimensional compressible inviscid flow past a LS89 blade at moderate Mach number, and a three-dimensional nonlinear mechanics problem to predict the long-time structural response of the standard section of a nuclear containment building under external loading.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-18DOI: 10.1186/s40323-024-00262-6
Hendrik Fischer, Julian Roth, Ludovic Chamoin, Amélie Fau, Mary Wheeler, Thomas Wick
In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the Biot system which consists of vector-valued displacements (geomechanics) coupled to a Darcy flow pressure equation. The MORe DWR method introduces a goal-oriented adaptive incremental proper orthogonal decomposition (POD) based-reduced-order model (ROM). The error in the reduced goal functional is estimated during the simulation, and the POD basis is enriched on-the-fly if the estimate exceeds a given threshold. This results in a reduction of the total number of full-order-model solves for the simulation of the porous medium, a robust estimation of the quantity of interest and well-suited reduced bases for the problem at hand. We apply a space-time Galerkin discretization with Taylor-Hood elements in space and a discontinuous Galerkin method with piecewise constant functions in time. The latter is well-known to be similar to the backward Euler scheme. We demonstrate the efficiency of our method on the well-known two-dimensional Mandel benchmark and a three-dimensional footing problem.
在这项工作中，针对多孔介质中的单相流问题，扩展并进一步发展了时空 MORe DWR（双加权残差误差估计的模型阶次缩减）框架。具体来说，我们的问题陈述是由矢量位移（地质力学）与达西流动压力方程耦合而成的 Biot 系统。MORe DWR 方法引入了一种以目标为导向、基于正交分解（POD）的自适应增量减阶模型（ROM）。在模拟过程中，对还原目标函数中的误差进行估算，如果估算值超过给定阈值，则对 POD 基础进行即时增强。这就减少了多孔介质模拟的全阶模型求解总数，对相关量进行了稳健的估计，并为当前问题提供了合适的简化基础。我们在空间采用了带有泰勒胡德元素的时空 Galerkin 离散化方法，在时间采用了带有片断常数函数的非连续 Galerkin 方法。众所周知，后者类似于后向欧拉方案。我们在著名的二维 Mandel 基准和三维地基问题上演示了我们方法的效率。
{"title":"Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity","authors":"Hendrik Fischer, Julian Roth, Ludovic Chamoin, Amélie Fau, Mary Wheeler, Thomas Wick","doi":"10.1186/s40323-024-00262-6","DOIUrl":"https://doi.org/10.1186/s40323-024-00262-6","url":null,"abstract":"In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the Biot system which consists of vector-valued displacements (geomechanics) coupled to a Darcy flow pressure equation. The MORe DWR method introduces a goal-oriented adaptive incremental proper orthogonal decomposition (POD) based-reduced-order model (ROM). The error in the reduced goal functional is estimated during the simulation, and the POD basis is enriched on-the-fly if the estimate exceeds a given threshold. This results in a reduction of the total number of full-order-model solves for the simulation of the porous medium, a robust estimation of the quantity of interest and well-suited reduced bases for the problem at hand. We apply a space-time Galerkin discretization with Taylor-Hood elements in space and a discontinuous Galerkin method with piecewise constant functions in time. The latter is well-known to be similar to the backward Euler scheme. We demonstrate the efficiency of our method on the well-known two-dimensional Mandel benchmark and a three-dimensional footing problem.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-15DOI: 10.1186/s40323-023-00257-9
Maximilian J. Grill, Wolfgang A. Wall, Christoph Meier
This article proposes a novel computational modeling approach for short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations, and gives a detailed overview how it fits into the framework of existing fiber or beam interaction models, either considering microscale molecular or macroscale contact effects. The direct evaluation of a molecular interaction potential between two general bodies in 3D space would require to integrate molecule densities over two 3D volumes, leading to a sixfold integral to be solved numerically. By exploiting the short-range nature of the considered class of interaction potentials as well as the fundamental kinematic assumption of undeformable fiber cross-sections, as typically applied in mechanical beam theories, a recently derived, closed-form analytical solution is applied for the interaction potential between a given section of the first fiber (slave beam) and the entire second fiber (master beam), whose geometry is linearly expanded at the point with smallest distance to the given slave beam section. This novel approach based on a pre-defined section–beam interaction potential (SBIP) requires only one single integration step along the slave beam length to be performed numerically. In addition to significant gains in computational efficiency, the total beam–beam interaction potential resulting from this approach is shown to exhibit an asymptotically consistent angular and distance scaling behavior. Critically for the numerical solution scheme, a regularization of the interaction potential in the zero-separation limit as well as the finite element discretization of the interacting fibers, modeled by the geometrically exact beam theory, are presented. In addition to elementary two-fiber systems, carefully chosen to verify accuracy and asymptotic consistence of the proposed SBIP approach, a potential practical application in form of adhesive nanofiber-grafted surfaces is studied. Involving a large number of helicoidal fibers undergoing large 3D deformations, arbitrary mutual fiber orientations as well as frequent local fiber pull-off and snap-into-contact events, this example demonstrates the robustness and computational efficiency of the new approach.
{"title":"Asymptotically consistent and computationally efficient modeling of short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations","authors":"Maximilian J. Grill, Wolfgang A. Wall, Christoph Meier","doi":"10.1186/s40323-023-00257-9","DOIUrl":"https://doi.org/10.1186/s40323-023-00257-9","url":null,"abstract":"This article proposes a novel computational modeling approach for short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations, and gives a detailed overview how it fits into the framework of existing fiber or beam interaction models, either considering microscale molecular or macroscale contact effects. The direct evaluation of a molecular interaction potential between two general bodies in 3D space would require to integrate molecule densities over two 3D volumes, leading to a sixfold integral to be solved numerically. By exploiting the short-range nature of the considered class of interaction potentials as well as the fundamental kinematic assumption of undeformable fiber cross-sections, as typically applied in mechanical beam theories, a recently derived, closed-form analytical solution is applied for the interaction potential between a given section of the first fiber (slave beam) and the entire second fiber (master beam), whose geometry is linearly expanded at the point with smallest distance to the given slave beam section. This novel approach based on a pre-defined section–beam interaction potential (SBIP) requires only one single integration step along the slave beam length to be performed numerically. In addition to significant gains in computational efficiency, the total beam–beam interaction potential resulting from this approach is shown to exhibit an asymptotically consistent angular and distance scaling behavior. Critically for the numerical solution scheme, a regularization of the interaction potential in the zero-separation limit as well as the finite element discretization of the interacting fibers, modeled by the geometrically exact beam theory, are presented. In addition to elementary two-fiber systems, carefully chosen to verify accuracy and asymptotic consistence of the proposed SBIP approach, a potential practical application in form of adhesive nanofiber-grafted surfaces is studied. Involving a large number of helicoidal fibers undergoing large 3D deformations, arbitrary mutual fiber orientations as well as frequent local fiber pull-off and snap-into-contact events, this example demonstrates the robustness and computational efficiency of the new approach.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140595721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-23DOI: 10.1186/s40323-024-00259-1
Davide Roznowicz, Giovanni Stabile, Nicola Demo, Davide Fransos, Gianluigi Rozza
The article presents the application of inductive graph machine learning surrogate models for accurate and efficient prediction of 3D flow for industrial geometries, explicitly focusing here on external aerodynamics for a motorsport case. The final aim is to build a surrogate model that can provide quick predictions, bypassing in this way the unfeasible computational burden of traditional computational fluid dynamics (CFD) simulations. We investigate in this contribution the usage of graph neural networks, given their ability to smoothly deal with unstructured data, which is the typical context for industrial simulations. We integrate an efficient subgraph-sampling approach with our model, specifically tailored for large dataset training. REV-GNN is the chosen graph machine learning model, that stands out for its capacity to extract deeper insights from neighboring graph regions. Additionally, its unique feature lies in its reversible architecture, which allows keeping the memory usage constant while increasing the number of network layers. We tested the methodology by applying it to a parametric Navier–Stokes problem, where the parameters control the surface shape of the industrial artifact at hand, here a motorbike.
{"title":"Large-scale graph-machine-learning surrogate models for 3D-flowfield prediction in external aerodynamics","authors":"Davide Roznowicz, Giovanni Stabile, Nicola Demo, Davide Fransos, Gianluigi Rozza","doi":"10.1186/s40323-024-00259-1","DOIUrl":"https://doi.org/10.1186/s40323-024-00259-1","url":null,"abstract":"The article presents the application of inductive graph machine learning surrogate models for accurate and efficient prediction of 3D flow for industrial geometries, explicitly focusing here on external aerodynamics for a motorsport case. The final aim is to build a surrogate model that can provide quick predictions, bypassing in this way the unfeasible computational burden of traditional computational fluid dynamics (CFD) simulations. We investigate in this contribution the usage of graph neural networks, given their ability to smoothly deal with unstructured data, which is the typical context for industrial simulations. We integrate an efficient subgraph-sampling approach with our model, specifically tailored for large dataset training. REV-GNN is the chosen graph machine learning model, that stands out for its capacity to extract deeper insights from neighboring graph regions. Additionally, its unique feature lies in its reversible architecture, which allows keeping the memory usage constant while increasing the number of network layers. We tested the methodology by applying it to a parametric Navier–Stokes problem, where the parameters control the surface shape of the industrial artifact at hand, here a motorbike.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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