A time-parallel framework for coupling finite element and lattice Boltzmann methods

International audienceIn this work we propose a new numerical procedure for the simulation of time-dependent problems based on the coupling between the finite element method and the lattice Boltzmann method. The procedure is based on the Parareal paradigm and allows to couple efficiently the two numerical methods, each one working with its own grid size and time-step size. The motivations behind this approach are manifold. Among others, we have that one technique may be more efficient, or physically more appropriate or less memory consuming than the other depending on the target of the simulation and/or on the sub-region of the computational domain. Furthermore, the coupling with finite element method may circumvent some difficulties inherent to lattice Boltzmann discretization, for some domains with complex boundaries, or for some boundary conditions. The theoretical and numerical framework is presented for parabolic equations, in order to describe and validate numerically the methodology in a simple situation

Fully discrete Heterogeneous Multiscale Method for parabolic problems with multiple spatial and temporal scales

The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual cell problem with an alternate one, using Dirichlet boundary and initial values instead of periodic boundary and time conditions. Further, we give a detailed a priori error analysis of the fully discretized, i.e., in space and time for both the macroscopic and the cell problem, method. Numerical experiments illustrate the theoretical convergence rates

G-CSC Report 2010

The present report gives a short summary of the research of the Goethe Center for Scientific Computing (G-CSC) of the Goethe University Frankfurt. G-CSC aims at developing and applying methods and tools for modelling and numerical simulation of problems from empirical science and technology. In particular, fast solvers for partial differential equations (i.e. pde) such as robust, parallel, and adaptive multigrid methods and numerical methods for stochastic differential equations are developed. These methods are highly adanvced and allow to solve complex problems.. The G-CSC is organised in departments and interdisciplinary research groups. Departments are localised directly at the G-CSC, while the task of interdisciplinary research groups is to bridge disciplines and to bring scientists form different departments together. Currently, G-CSC consists of the department Simulation and Modelling and the interdisciplinary research group Computational Finance

Integration of 3D geological and numerical models based on tetrahedral meshes for hydrogeological simulations in fractured porous media

Une nouvelle approche de modélisation des milieux géologiques fracturés représentés par un modèle conceptuel de fractures discrètes et déterministes est présentée dans cette thèse. L'objectif principal de l'étude est de reproduire l'hétérogénéité et la complexité des milieux poreux fracturés dans un modèle géométrique tridimensionnel afin d'effectuer des simulations numériques dans le but d'améliorer les capacités de modélisation en hydrogéologie. Ceci est réalisé à travers le couplage entre une plateforme de modélisation géologique (GOCAD) et un code numérique (HydroGeoSphere). Les principaux défis à relever sont: la représentation géométrique du réseau de fractures, la sélection d'un maillage approprié pour la discrétisation spatiale du domaine de simulation et l'adaptation du code numérique à ce maillage. La nouvelle approche est basée sur une première phase de modélisation géologique 3D, suivie par la génération d'un maillage tétraédrique 3D et par la simulation numérique de l'écoulement souterrain en conditions saturées et du transport de solutés. En général, le maillage tétraédrique s'avère plus adéquat que les maillages de blocs ou de prismes pour discrétiser les geometries complexes telles que les milieux fracturés. De plus, une définition alternative du maillage "dual", qui est essentiel pour appliquer la méthode numérique élément finis - volume de contrôle utilisée par HydroGeoSphere, est analysée et intégrée dans le code numérique. Le code numérique proposé est d'abord vérifié par l'intermédiaire de simples scénarios de simulation dont les solutions, analytiques et numériques, sont déjà connues. La complexité des simulations est augmentée de façon graduelle. L'approche de modélisation est finalement appliquée au site Olkiluoto (Finlande) où un laboratoire de recherche souterrain est en construction afin d'évaluer la faisabilité du stockage géologique profond de déchets nucléaires à haute activité. Les techniques de modélisation géologique mises au point permettent de modéliser facilement la géométrie des fractures identifiées à travers la caractérisation géologique in situ. De plus, le modèle numérique s'avère adéquat pour la simulation de l'écoulement et du transport de solutés dans ce site complexe. Ce travail de recherche présente une contribution au développement des techniques de modélisation hydrogéologique des milieux fracturés

Euratom Contribution to the Generation IV International Forum Systems in the period 2005-2014 and future outlook

The "Generation IV International Forum" (GIF) is a nuclear-related research and development international programme launched in 2001. GIF is organized into, six reactor system arrangements (SA) and within each system arrangement, specific project arrangements (PA) exist. The six reactor systems are: Sodium-cooled Fast Reactor (SFR); Lead-cooled Fast Reactor (LFR); Very High-Temperature Reactor (VHTR); Gas-Cooled Fast Reactor (GFR); Supercritical Water-Cooled Reactor (SCWR); Molten Salt Reactor (MSR). In addition, three cross-cutting methodology working groups (MWG) were created on Economic Modelling (EMWG), Proliferation Resistance and Physical Protection (PRPPWG), and on Risk and Safety (RSWG). On the basis of an EU Commission Decision, Euratom adhered to GIF by signing in July 2003 the "Charter of the Generation IV Forum". Euratom then acceded to the International "Framework Agreement" among the Members of the Generation IV International Forum. The Joint Research Centre (JRC) of the European Commission is the Implementing Agent for Euratom within GIF. France is participating as an individual full member within GIF and only brief information will be given to complement any specific GIF reporting provided by France. Euratom has been contributing to all six systems to allow all Member States (MS) to allow any contribution and sharing of research results in specific systems of their choice as EU Member States (MS) are responsible of their own national energy mix strategy by including nuclear (or not) within their energy mix.JRC.A.7-Euratom Coordinatio

A Computationally Efficient Hybrid Neural Network Architecture for Porous Media: Integrating CNNs and GNNs for Improved Permeability Prediction

Subsurface fluid flow, essential in various natural and engineered processes, is largely governed by a rock's permeability, which describes its ability to allow fluid passage. While convolutional neural networks (CNNs) have been employed to estimate permeability from high-resolution 3D rock images, our novel visualization technology reveals that they occasionally miss higher-level characteristics, such as nuanced connectivity and flow paths, within porous media. To address this, we propose a novel fusion model to integrate CNN with the graph neural network (GNN), which capitalizes on graph representations derived from pore network model to capture intricate relational data between pores. The permeability prediction accuracy of the fusion model is superior to the standalone CNN, whereas its total parameter number is nearly two orders of magnitude lower than the latter. This innovative approach not only heralds a new frontier in the research of digital rock property predictions, but also demonstrates remarkable improvements in prediction accuracy and efficiency, emphasizing the transformative potential of hybrid neural network architectures in subsurface fluid flow research

NASA SBIR abstracts of 1991 phase 1 projects

The objectives of 301 projects placed under contract by the Small Business Innovation Research (SBIR) program of the National Aeronautics and Space Administration (NASA) are described. These projects were selected competitively from among proposals submitted to NASA in response to the 1991 SBIR Program Solicitation. The basic document consists of edited, non-proprietary abstracts of the winning proposals submitted by small businesses. The abstracts are presented under the 15 technical topics within which Phase 1 proposals were solicited. Each project was assigned a sequential identifying number from 001 to 301, in order of its appearance in the body of the report. Appendixes to provide additional information about the SBIR program and permit cross-reference of the 1991 Phase 1 projects by company name, location by state, principal investigator, NASA Field Center responsible for management of each project, and NASA contract number are included

The Mechanical Behavior of Salt X

Rock salt formations have long been recognized as a valuable resource - not only for salt mining but for construction of oil and gas storage caverns and for isolation of radioactive and other hazardous wastes. Current interest is fast expanding towards construction and re-use of solution-mined caverns for storage of renewable energy in the form of hydrogen, compressed air and other gases. Evaluating the long term performance and safety of such systems demands an understanding of the coupled mechanical behavior and transport properties of salt. This volume presents a collection of 60 research papers defining the state-of-the-art in the field. Topics range from fundamental work on deformation mechanisms and damage of rock salt to compaction of engineered salt backfill. The latest constitutive models are applied in computational studies addressing the evolution and integrity of storage caverns, repositories, salt mines and entire salt formations, while field studies document ground truth at multiple scales. The volume is structured into seven themes: Microphysical processes and creep models Laboratory testing Geological isolation systems and geotechnical barriers Analytical and numerical modelling Monitoring and site-specific studies Cavern and borehole abandonment and integrity Energy storage in salt caverns The Mechanical Behavior of Salt X will appeal to graduate students, academics, engineers and professionals working in the fields of salt mechanics, salt mining and geological storage of energy and wastes, but also to researchers in rock physics in general