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Existence of weak solutions for a nonlocal pseudo-parabolic model for Brinkman two-phase flow in asymptotically flat porous media

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arXiv 2018年

作者： Armiti-Juber, Alaa Rohde, Christian Institute for Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 Stuttgart70569 Germany

We study a nonlocal evolution equation that involves a pseudo-parabolic third-order term. The equation models almost uni-directional two-phase flow in Brinkman regimes. We prove the existence of weak solutions for this equation. We also give a series of numerical examples that demonstrate the ability of the equation to support overshooting like in [12] and explore the behavior of solutions in various limit regimes. Copyright © 2018, The Authors. All rights reserved.

关键词： Two phase flow

Greedy kernel methods for center manifold approximation

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arXiv 2018年

作者： Hamzi, B. Haasdonk, B. Santin, G. Wittwar, D. Department of Mathematics AlFaisal University Riyadh Saudi Arabia Institute for Applied Analysis and Numerical Simulation University of Stuttgart Germany

For certain dynamical systems it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows to isolate the complicated asymptotic behavior of the system close to a non-hyperbolic equilibrium point, and to obtain meaningful predictions of its behavior by analyzing a reduced dimensional problem. Since the manifold is usually not known, approximation methods are of great interest to obtain qualitative estimates. In this work, we use a data-based greedy kernel method to construct a suitable approximation of the manifold close to the equilibrium. The data are collected by repeated numerical simulation of the full system by means of a high-accuracy solver, which generates sets of discrete trajectories that are then used to construct a surrogate model of the manifold. The method is tested on different examples which show promising performance and good accuracy. Copyright © 2018, The Authors. All rights reserved.

关键词： Dynamical systems

Enabling interactive mobile simulations through distributed reduced models

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arXiv 2018年

作者： Dibaka, Christoph Haasdonkb, Bernard Schmidtb, Andreas Durra, Frank Rothermela, Kurt Institute of Parallel and Distributed Systems University of Stuttgart Stuttgart Germany Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany

Currently, various hardware and software companies are developing augmented reality devices, most prominently Microsoft with its Hololens. Besides gaming, such devices can be used for serious pervasive applications, like interactive mobile simulations to support engineers in the field. Interactive simulations have high demands on resources, which the mobile device alone is unable to satisfy. Therefore, we propose a framework to support mobile simulations by distributing the computation between the mobile device and a remote server based on the reduced basis method. Evaluations show that we can speed-up the numerical computation by over 131 times while using 73 times less energy. Copyright © 2018, The Authors. All rights reserved.

关键词： Augmented reality

numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods

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arXiv 2018年

作者： Köppl, Tobias Helmig, Rainer Santin, Gabriele Haasdonk, Bernard University of Stuttgart Department of Hydromechanics and Modelling of Hydrosystems Pfaffenwaldring 61 Germany University of Stuttgart Institute of Applied Analysis and Numerical Simulation Pfaffenwaldring 57 Germany

In this work, we consider two kinds of model reduction techniques to simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery i.e. in an artery that is located far away from the heart. For our simulations we place the stenosis in one of the tibial arteries belonging to the right lower leg (right post tibial artery). The model reduction techniques that are used are on the one hand dimensionally reduced models (1-D and 0-D models, the so-called mixed-dimension model) and on the other hand surrogate models produced by kernel methods. Both methods are combined in such a way that the mixed-dimension models yield training data for the surrogate model, where the surrogate model is parametrised by the degree of narrowing of the peripheral stenosis. By means of a well-trained surrogate model, we show that simulation data can be reproduced with a satisfactory accuracy and that parameter optimisation or state estimation problems can be solved in a very efficient way. Furthermore it is demonstrated that a surrogate model enables us to present after a very short simulation time the impact of a varying degree of stenosis on blood flow, obtaining a speedup of several orders over the full model. Copyright © 2018, The Authors. All rights reserved.

关键词： Hemodynamics

hp-multilevel monte carlo methods for uncertainty quantification of compressible flows

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arXiv 2018年

作者： Beck, Andrea Dürrwachter, Jakob Kuhn, Thomas Meyer, Fabian Munz, Claus-Dieter Rohde, Christian Institute of Aerodynamics and Gas Dynamics University of Stuttgart Pfaffenwaldring 21 Stuttgart70569 Germany Institute of Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 Stuttgart70569 Germany

We propose a novel hp-Multilevel Monte Carlo method for the quantification of uncertainties in compressible flows using the Discontinuous Galerkin method as deterministic solver. The multilevel approach exploits hierarchies of uniformly refined meshes jointly with an increasing polynomial degree for the ansatz space. It allows for a very large range of resolutions in the physical space and thus an efficient decrease of the statistical error. We prove that the overall complexity of the hp-Multilevel Monte Carlo method to compute the mean field with prescribed accuracy is of quadratic order with respect to the accuracy. We also propose a novel and simple approach to estimate a lower confidence bound for the optimal number of samples per level, which helps to prevent overshooting the optimal number of samples. The method is in particular adapted to the needs of high-performance computing. Our theoretical results are verified by numerical experiments for the two dimensional compressible Navier-Stokes equations. In particular we consider a cavity flow problem from computational acoustics, demonstrating that the method is suitable to handle complex engineering *** Codes 35R60, 65C05, 65M60 Copyright © 2018, The Authors. All rights reserved.

关键词： Monte Carlo methods

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

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arXiv 2020年

作者： Berre, Inga Boon, Wietse M. Flemisch, Bernd Fumagalli, Alessio Gläser, Dennis Keilegavlen, Eirik Scotti, Anna Stefansson, Ivar Tatomir, Alexandru Brenner, Konstantin Burbulla, Samuel Devloo, Philippe Duran, Omar Favino, Marco Hennicker, Julian Lee, I-Hsien Lipnikov, Konstantin Masson, Roland Mosthaf, Klaus Chiara Nestola, Maria Giuseppina Ni, Chuen-Fa Nikitin, Kirill Schädle, Philipp Svyatskiy, Daniil Yanbarisov, Ruslan Zulianp, Patrick Department of Mathematics University of Bergen Allégaten 41 Bergen5007 Norway Department of Mathematics KTH Royal Institute of Technology Lindstedtsvägen 25 Stockholm11428 Sweden Department of Hydromechanics and Modelling of Hydrosystems University of Stuttgart Pfaffenwaldring 61 Stuttgart70569 Germany Laboratory for Modeling and Scientific Computing MOX Politecnico di Milano p.za Leonardo da Vinci 32 Milano20133 Italy Department of Applied Geology Geosciences Center University of Göttingen Goldschmidtstrasse 3 Göttingen37077 Germany Department of Earth Sciences Uppsala University Villavägen 16 UppsalaS-75236 Sweden University of Côte d’Azur CNRS INRIA LJAD Nice France Institute of Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 Stuttgart70569 Germany FEC Universidade Estadual de Campinas Cidade Universitária R. Josiah Willard Gibbs 85 Campinas-SPCEP 13083-839 Brazil Institute of Earth Sciences University of Lausanne Building Geopolis UNIL-Mouline Lausanne1015 Switzerland Section de Mathématiques Université de Genève 2-4 rue du Lièvre CP 64 Genève1211 Switzerland Graduate Institute of Applied Geology National Central University Taiwan Center for Environmental Studies National Central University Taiwan Los Alamos National Laboratory New Mexico United States Department of Environmental Engineering Technical University of Denmark Bygningstorvet Building 115 Kgs. Lyngby2800 Denmark Numerical Simulation in Science Medicine and Engineering Group Institute of Computational Science Università della Svizzera italiana. Via G. Buffi 13 Lugano Ticino6900 Switzerland Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences Moscow Russia ETH Zürich Geothermal Energy and Geofluids Group Institute of Geophysics Zürich8092 Switzerland

Flow in fractured porous media occurs in the earth’s subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, we present a portfolio of four benchmark cases for single-phase flow in three-dimensional fractured porous media. The cases are specifically designed to test the methods’ capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases. Copyright © 2020, The Authors. All rights reserved.

关键词： numerical methods

Exa-Dune - Flexible PDE solvers, numerical methods and applications

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arXiv 2019年

作者： Bastian, Peter Altenbernd, Mirco Dreier, Nils-Arne Engwer, Christian Fahlke, Jorrit Fritze, René Geveler, Markus Göddeke, Dominik Iliev, Oleg Ippisch, Olaf Mohring, Jan Müthing, Steffen Ohlberger, Mario Ribbrock, Dirk Shegunov, Nikolay Turek, Stefan Interdisciplinary Center for Scientific Computing Heidelberg University Im Neuenheimer Feld 368 HeidelbergD-69120 Institute for Analysis and Numerics University of Münster Orleans-Ring 10 MünsterD-48149 Institute for Applied Analysis and Numerical Simulation University of Stuttgart Allmandring 5b StuttgartD-70569 Inst. f. Applied Mathematics TU Dortmund Vogelpothsweg 87 DortmundD-44227 Germany Fraunhofer Institute for Industrial Mathematics ITWM Fraunhofer-Platz 1 KaiserslauterD-67663 Germany Institut für Mathematik TU Clausthal-Zellerfeld Erzstr. 1 Clausthal-ZellerfeldD-38678 Germany

In the Exa-Dune project we have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively parallel architecture. In order to cope with the increased probability of hardware failures, one aim of the project was to add flexible, application-oriented resilience capabilities into the framework. Continuous improvement of the underlying hardware-oriented numerical methods have included GPU-based sparse approximate inverses, matrix-free sum-factorisation for high-order discontinuous Galerkin discretisations as well as partially matrix-free preconditioners. On top of that, additional scalability is facilitated by exploiting massive coarse grained parallelism offered by multiscale and uncertainty quantification methods where we have focused on the adaptive choice of the coarse/fine scale and the overlap region as well as the combination of local reduced basis multiscale methods and the multilevel Monte-Carlo algorithm. Finally, some of the concepts are applied in a land-surface model including subsurface flow and surface runoff. Copyright © 2019, The Authors. All rights reserved.

关键词： numerical methods

Towards realistic HPC models of the neuromuscular system

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arXiv 2018年

作者： Bradley, Chris Emamy, Nehzat Ertl, Thomas Göddeke, Dominik Hessenthaler, Andreas Klotz, Thomas Krämer, Aaron Krone, Michael Maier, Benjamin Mehl, Miriam Rau, Tobias Röhrle, Oliver SimTech Research Group on Continuum Biomechanics and Mechanobiology University of Stuttgart Institute for Applied Analysis and Numerical Simulation University of Stuttgart Institute for Parallel and Distributed Systems University of Stuttgart University of Stuttgart Stuttgart Centre for Simulation Sciences University of Stuttgart Germany Auckland Bioengineering Institute University of Auckland New Zealand

Realistic simulations of detailed, biophysics-based, multi-scale models require very high resolution and, thus, large-scale compute facilities. Existing simulation environments, especially for biomedical applications, are designed to allow for a high flexibility and generality in model development. Flexibility and model development, however, are often a limiting factor for large-scale simulations. Therefore, new models are typically tested and run on small-scale compute facilities. By using a detailed biophysics-based, chemo-electromechanical skeletal muscle model and the international open-source software library OpenCMISS as an example, we present an approach to upgrade an existing muscle simulation framework from a moderately parallel version towards a massively parallel one that scales both in terms of problem size and in terms of the number of parallel processes. For this purpose, we investigate different modeling, algorithmic and implementational aspects. We present improvements addressing both numerical and parallel scalability. In addition, our approach includes a novel visualization environment, which is based on the MegaMol environment capable of handling large amounts of simulated data. It offers a platform for fast visualization prototyping, distributed rendering, and advanced visualization techniques. We present results of a variety of scaling studies at the Tier-1 supercomputer HazelHen at the High Performance Computing Center Stuttgart (HLRS). We improve the overall runtime by a factor of up to 2.6 and achieved good scalability on up to 768 cores, where the previous implementation used only 4 *** Codes 65L99, 65M99 Copyright © 2018, The Authors. All rights reserved.

关键词： Scalability

simulation of seismic responses from the 3D non-linear model of the Bazhenov formation

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IOP Conference Series: Materials Science and Engineering 2020年第1期927卷

作者： I S Nikitin V I Golubev A V Ekimenko M B Anosova Department of Mathematical Simulation Institute of Computer Aided Design of RAS 19/18 2-nd Brestskaya str. Moscow 123056 Russia Laboratory of Applied Numerical Geophysics Moscow Institute of Physics and Technology 9 Institutskiy per. Dolgoprudny Moscow Region 141701 Russia Seismic Data Analysis Department Gazprom Neft Science & Technology Centre Moika river embankment 75-79 Saint Petersburg 190000 Russia

The article is devoted to the investigation of seismic responses from probable oil-bearing formations. The three-dimensional geological model of the Bazhenov formation situated at Western Siberia is constructed. It is based on the elastic two-dimensional cross-section with curvilinear boundaries between different layers. For this purpose, logging and seismic data were processed jointly. To describe correctly the internal structure of mudstones the novel continuum model of media with interlayer slippage and delamination was utilized. The grid-characteristic method was used to solve numerically the govern system of the linear elasticity. The non-linearity of the model is incorporated with the appropriate explicit-implicit approximation procedure. For increasing the reliability of obtained synthetic seismograms the presence of the static rock pressure was taken into account. Reasonable computational time was achieved with the help of the parallelization based on the Message Passing Interface (MPI) technology. To analyze the structure of seismic responses wave patterns for the model with different parameters were presented. The influence of fractured layer on registered seismic traces were estimated. The proposed numerical approach may be used for simulation of complex geological objects.

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