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Dispersion in Shallow Moment Equations

Communications on Applied Mathematics and Computation 2024年第4期6卷 2155-2195页

作者： Ullika Scholz Julia Kowalski Manuel Torrilhon Applied and Computational Mathematics(ACoM) RWTH Aachen UniversityAachenGermany Methods for Model‑based Development in Computational Engineering(MBD) RWTH Aachen UniversityAachenGermany

Shallow moment models are extensions of the hyperbolic shallow water *** admit variations in the vertical profile of the horizontal *** paper introduces a non-hydrostatic pressure to this framework and shows the systematic derivation of dimensionally reduced dispersive equation systems which still hold information on the vertical profiles of the flow *** derivation from a set of balance laws is based on a splitting of the pressure followed by a same-degree polynomial expansion of the velocity and pressure fields in a vertical *** reduction is done via Galerkin projections with weak enforcement of the boundary conditions at the bottom and at the free *** resulting equation systems of order zero and one are presented in linear and nonlinear forms for Legendre basis functions and an analysis of dispersive properties is given.A numerical experiment shows convergence towards the resolved reference model in the linear stationary case and demonstrates the reconstruction of vertical profiles.

关键词： Shallow flow Free surface flow Non-hydrostatic model Dispersive equations Moment approximation Hyperbolic systems

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A Classification Method for the Systematic Identification of models and Workflows in MBSE 33

A Classification Method for the Systematic Identification of...

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33rd Symposium Design for X, DFX 2022

作者： Hoepfner, Gregor Kowalski, Julia Faustmann, Clemens Zerwas, Thilo Kranabitl, Philipp Vafaei, Seyedmohammad Jacobs, Georg Hick, Hannes Institute for Machine Elements and Systems Engineering RWTH Aachen University Germany Methods for Model-based Development in Computational Engineering RWTH Aachen University Germany Institute of Machine Components and Methods of Development TU Graz Austria

Modern engineering uses models for virtual verification of systems. Such models are usually combined in workflows, where the results of models are linked to verify system requirements. model-based Systems engineering (MBSE) has evolved as an approach to ease the usage of models and workflows. One goal in MBSE is to reuse models and workflows from libraries. However, the step of identifying and classifying both models and workflows for such a library is not yet systematized. We propose a method on how to identify models and workflows for an MBSE model library. Possible purposes of models are identified and afterwards models satisfying that purpose are retrieved. The identified models are systematically combined to workflows. Thereby a systematic approach to create a model library is given. © 2022 die Autoren.

关键词： Libraries

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Consistent splitting SAV schemes for finite element approximations of incompressible flows

arXiv

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arXiv 2025年

作者： Pacheco, Douglas R.Q. Chair for Computational Analysis of Technical Systems RWTH Aachen University Germany Chair of Methods for Model-based Development in Computational Engineering RWTH Germany RWTH Aachen University Germany

Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when finite elements are used for the spatial discretisation. This work proposes a simple scalar auxiliary variable (SAV) technique that, when combined with standard finite elements in space, guarantees unconditional stability for first- and second-order consistent splitting schemes. The framework is implicit-explicit (IMEX) and only requires solving linear transport equations and a pressure Poisson problem per time step. Furthermore, pressure stability is attained with respect to a stronger norm than in classical projection schemes, which allows eliminating the inf-sup compatibility requirement on the velocity-pressure pairs. The accuracy of the new framework is assessed through numerical examples. © 2025, CC BY.

关键词： Incompressible flow

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Fully consistent lowest-order finite element methods for generalised Stokes flows with variable viscosity

arXiv

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arXiv 2024年

作者： Galarce, Felipe Pacheco, Douglas R.Q. School of Civil Engineering Pontificia Universidad Católica de Valparaíso Chile Computational Analysis of Technical Systems RWTH Aachen University Germany Methods for Model-based Development in Computational Engineering RWTH Germany RWTH Aachen University Germany

Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for incompressible flows, the most popular approach to allow equal-order velocity-pressure interpolation are residual-based stabilisations. For low-order elements, however, the viscous part of that residual cannot be approximated, often compromising accuracy. Assuming slightly more regularity on the viscosity field, we can construct stabilisation methods that fully approximate the residual, regardless of the polynomial order of the finite element spaces. This work analyses two variants of this fully consistent approach, with the generalised Stokes system as a model problem. We prove unique solvability and derive expressions for the stabilisation parameter, generalising some classical results for constant viscosity. Numerical results illustrate how our method completely eliminates the spurious pressure boundary layers typically induced by low-order PSPG-like stabilisations. Copyright © 2024, The Authors. All rights reserved.

关键词： Stabilization

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Heat recovery and thermal energy storage potential using buried infrastructure in the UK

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Proceedings of the Institution of Civil Engineers: Smart Infrastructure and Construction 2022年第1期175卷 10-26页

作者： Loveridge, Fleur Schellart, Alma Rees, Simon Stirling, Ross Taborda, David Tait, Simon Alibardi, Luca Biscontin, Giovanna Shepley, Paul Shafagh, Ida Shepherd, Will Yildiz, Anil Jefferson, Bruce School of Civil Engineering University of Leeds Leeds United Kingdom Department of Civil and Structural Engineering University of Sheffield Sheffield United Kingdom School of Engineering Newcastle University Newcastle upon Tyne United Kingdom Cranfield Water Science Institute Cranfield University Cranfield United Kingdom Schofield Centre Department of Engineering University of Cambridge Cambridge United Kingdom Methods for Model-based Development in Computational Engineering Rwth Aachen University Aachen Germany

Dispersed space heating alone accounts for 40% of UK energy use and 20% of carbon dioxide (CO2) emissions. Tackling heating and building cooling demands is therefore critical to achieve net-zero ambitions in the UK. The most energy-efficient way to reduce the carbon dioxide emissions of heating and cooling is through the use of ground-source heat pumps and district heating technology. However, capital costs are often high, sometimes prohibitively so. To reduce investment costs, it is proposed to use buried infrastructure as sources and stores of thermal energy. Barriers to this innovative approach include lack of knowledge about the actual net amount of recoverable energy and impacts on the primary function of any buried infrastructure, as well as the need for new investment and governance strategies integrated across the energy and infrastructure sectors. Additional opportunities from thermal utilisation in buried infrastructure include the potential mitigation of damaging biological and/or chemical processes that may occur. This paper presents a first assessment of the scale of the opportunity for thermal energy recovery and storage linked to new and existing buried infrastructure, along with strategic measures to help reduce barriers and start the UK on the journey to achievement of its infrastructure energy potential. © 2022 ICE Publishing: All rights reserved.

关键词： Thermal energy

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Unconditionally stable, linearised IMEX schemes for incompressible flows with variable density

arXiv

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arXiv 2024年

作者： Espinoza-Contreras, Nicolás Barrenechea, Gabriel R. Castillo, Ernesto Pacheco, Douglas R.Q. Computational Analysis of Technical Systems RWTH Aachen University Germany Methods for Model-based Development in Computational Engineering RWTH Germany RWTH Aachen University Germany Department of Mathematics and Statistics University of Strathclyde Glasgow United Kingdom Department of Mechanical Engineering University of Santiago de Chile Santiago Chile

For the incompressible Navier–Stokes system with variable density and viscosity, we propose and analyse an IMEX framework treating the convective and diffusive terms semi-implicitly. This extends to variable density and second order in time some methods previously analysed for variable viscosity and constant density. We present three new schemes, both monolithic and fractional-step. All of them share the methodological novelty that the viscous term is treated in an implicit-explicit (IMEX) fashion, which allows decoupling the velocity components. Unconditional temporal stability is proved for all three variants. Furthermore, the system to solve at each time step is linear, thus avoiding the costly solution of nonlinear problems even if the viscosity follows a non-Newtonian rheological law. Our presentation is restricted to the semi-discrete case, only considering the time discretisation. In this way, the results herein can be applied to any spatial discretisation. We validate our theory through numerical experiments considering finite element methods in space. The tests range from simple manufactured solutions to complex two-phase viscoplastic flows. © 2024, CC BY.

关键词： Non Newtonian flow

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Deep-learning surrogate models for the stability of a wide rectangular tunnel

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Computers and Geotechnics 2025年 179卷

作者： Nguyen, H.C. Xu, H. Nazem, M. Sousa, R. Kowalski, J. Zhao, Q. Formerly Department of Civil and Environmental Engineering Imperial College London London United Kingdom Methods for Model-based Development in Computational Engineering RWTH Aachen University Aachen Germany School of Civil Engineering and Architecture Xi'an University of Technology China Department of Civil and Infrastructure Engineering School of Engineering RMIT University Melbourne Australia New York University Abu Dhabi Abu Dhabi United Arab Emirates

The stability of a wide rectangular tunnel in spatially variable soils is investigated using deep-learning surrogate models combined with a mixed formulation of limit analysis. The mixed formulation is employed to perform stochastic simulations of tunnels in spatially random soils, generating the data to train the surrogate models. Two types of deep-learning models are tested: Fully Connected Neural Networks (FCNs) and Convolutional Neural Networks (CNNs). To enhance model performance, the study introduces two novel encoding techniques to enhance the identification of tunnel regions in the input data. The first, Mask-FCN, directly incorporates spatial information into the model by adding a binary mask layer to distinguish tunnel regions from the surrounding soil. The second, Grad-FCN, modifies training gradients to indirectly highlight these differences. Additionally, a Mask-CNN model is developed, leveraging spatial filtering to better capture local patterns and correlations. Our results show that the surrogate models, trained on data from stochastic reliability analyses, demonstrate robustness and accuracy across various evaluation metrics. The encoding neural networks outperform the baseline model in accuracy and overall regression performance on training datasets. Importantly, both encoding networks achieve acceptable accuracy on unseen datasets with new tunnel geometric features, a task the baseline model fails to accomplish. The FCN-based encoding neural network achieves prediction capabilities comparable to ordinary CNNs, while the CNN-based encoding neural network delivers high prediction accuracy for unknown datasets with new tunnel geometric characteristics. The study concludes that the generated surrogate models offer a computationally efficient alternative for predicting tunnel stability in spatially variable soils. © 2024 Elsevier Ltd

关键词： Convolutional neural networks

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Deep Learning for the Stability of Spatially Variable Slopes

SSRN

引用

SSRN 2024年

作者： Nguyen, Hoang C. Xu, Haoding He, Xuzhen Kowalski, Julia Faculty of Civil Engineering Architecture Xi’an University of Technology China Formerly Department of Civil and Environmental Engineering Imperial College London London United Kingdom School of Civil and Environmental Engineering University of Technology SydneyNSW2007 Australia Methods for Model-based Development in Computational Engineering RWTH Aachen University Aachen Germany

In this paper, we present deep-learning surrogate models to replace stochastic simulations of the stability of slopes in spatially variable soils. This study is the first to employ machine learning to enhance the stochastic analysis of slopes with consideration of seismic effects. In particular, stochastic simulations of slope stability are conducted using a mixed formulation of limit analysis, providing data to feed various machine learning algorithms to build surrogate models to replace numerical simulations. The results reconfirm that convolutional neural networks (CNNs) and fully connected neural networks (FCNs) effectively handle multiple uncertainties and efficiently predict the values of the safety factor of good agreement with the benchmarking results obtained using other numerical approaches. Deep-learning surrogate models empower stochastic analysis by improving computational efficiency. It takes several hours to get all statistical descriptions of safety factors for $1000$ numerical simulations. However, deep-learning surrogate models only need several minutes to provide such information with highly accurate values. © 2024, The Authors. All rights reserved.

关键词： Safety factor

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Interaction between capabilities of model based Systems engineering on sensor models

Interaction between capabilities of Model Based Systems Engi...

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IEEE International Symposium on Systems engineering (ISSE)

作者： Marvin Michael Schmidt Simon Schmidt Rainer Stark Model Based Engineering Fraunhofer IPK Berlin Germany Methods Development Volkswagen AG Wolfsburg Germany Industrial Information Technology TU Berlin Berlin Germany

In modern product development, models are often used for different purposes, e.g., system synthesis, trade-off analysis of system parameters or visualization and creation of design concepts. For some models, this purpose as well as the model itself might change over time. New interactions with the target system can occur and new details are added over time. Both have to be integrated immediately into the development procedure. When models are not maintained up to date and not used by different stakeholders, the benefits of the model-based approach are lessened due to the effort for generation and maintenance. The five development capabilities of MBSE, comprising Systems Environment Analytics (SEA), Systems Definition and Derivation (SDD), Systems Interaction modeling (SIM), Systems Lifecycle engineering (SLE) and the MBSE Capability and Maturation Matrix (CMM) address this topic on a capability *** this article, the authors point out the interaction between these development capabilities on the example of a Pedestrian Emergency Braking System (PEBS) development in automotive industry, with a focus on sensor models. It will be shown exemplary how one development capability might influence another and how this interaction supports the development of complex systems.

关键词： Industries Analytical models Visualization Machine learning Maintenance engineering Tools Product development

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modeling and simulating transient close-contact melting via space-time finite elements

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AIP Conference Proceedings 2024年第1期3034卷

作者： Leonardo Boledi Stefanie Elgeti Julia Kowalski Chair of Methods for Model-based Development in Computational Engineering (MBD) RWTH Aachen University 52056 Aachen Germany Institute of Lightweight Design and Structural Biomechanics (ILSB) TU Wien 1060 Vienna Austria Chair for Computational Analysis of Technical Systems (CATS) RWTH Aachen University 52056 Aachen Germany

Close-contact melting phenomena occur when a heated body is in contact with a solid phase-change material. Deter-mining the velocity at which the heat source melts through the solid is fundamental to investigate the process and extrapolate it to operating conditions that cannot be replicated by experiments. Available results in the literature consider a thermo-mechanical equilibrium in the contact film and thus derive a constant melting *** this work we relax this assumption and present a transient contact melting model for a planar heat source. After solving for the heat equation in the solid phase with a space-time finite element approach, the transient heat flux around the heated body is used to compute the time-dependent melting velocity. With the latter we can update the computational domain via a mesh-update method, so that the displacement of the heat source is represented over *** demonstrate the potential of our approach, we introduce a numerical example with a 2D test case. Afterwards, we show the evolving position of the heat source and we compare the transient melting velocity against the equilibrium estimate. A more complex time-dependent input power is then considered in view of realistic applications.

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