Localized Computation of Newton Updates in Fully-implicit Two-phase Flow Simulation

AbstractFully-Implicit (FI) Methods are often employed in the numerical simulation of large-scale subsurface flows in porous media. At each implicit time step, a Newton-like method is used to solve the FI discrete nonlinear algebraic system. The linear solution process for the Newton updates is the computational workhorse of FI simulations. Empirical observations suggest that the computed Newton updates during FI simulations of multiphase flow are often sparse. Moreover, the level of sparsity observed can vary dramatically from iteration to the next, and across time steps. In several large scale applications, it was reported that the level of sparsity in the Newton update can be as large as 99%. This work develops a localization algorithm that conservatively predetermines the sparsity pattern of the Newton update. Subsequently, only the flagged nonzero components of the system need be solved. The localization algorithm is developed for general FI models of two phase flow. Large scale simulation results of benchmark reservoir models show a 10 to 100 fold reduction in computational cost for homogeneous problems, and a 4 to 10 fold reduction for strongly heterogeneous problems

Intermittency and Self-Organisation in Turbulence and Statistical Mechanics

There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramatically enhancing transport. A proper description of this intermittent phenomenon, however, is extremely difficult, requiring a new non-perturbative theory, such as statistical description. Furthermore, multi-scale interactions are responsible for inevitably complex dynamics in strongly non-equilibrium systems, a proper understanding of which remains a main challenge in classical physics. As a remarkable consequence of multi-scale interaction, a quasi-equilibrium state (the so-called self-organisation) can however be maintained. This special issue aims to present different theories of statistical mechanics to understand this challenging multiscale problem in turbulence. The 14 contributions to this Special issue focus on the various aspects of intermittency, coherent structures, self-organisation, bifurcation and nonlocality. Given the ubiquity of turbulence, the contributions cover a broad range of systems covering laboratory fluids (channel flow, the Von Kármán flow), plasmas (magnetic fusion), laser cavity, wind turbine, air flow around a high-speed train, solar wind and industrial application

Phase-field modeling of unidirectionally solidified microstructures under diffusive-convective regime

Moderne Werkstoffe zeichnen sich oft durch ein breites Spektrum an maßgeschneiderten mechanischen, magnetischen, elektronischen oder thermophysikalischen Eigenschaften aus. In Verbindung mit der ihnen zugrundeliegenden Mikrostruktur kann das Verhalten der meisten technischen Werkstoffe durch genaue Modellierung der neuartigen Eigenschaften mit maßgeschneiderten Morphologien vorhergesagt werden. Im Allgemeinen wird die Bildung von Erstarrungsmikrostrukturen durch das Wechselspiel zwischen Kapillarität und Diffusion bestimmt. Das Vorhandensein von Schmelzekonvektion spielt eine bedeutende Rolle für die endgültigen Gefügeeigenschaften von Gusslegierungen und wird aufgrund seiner Komplexität oft vernachlässigt. Da die Kontrolle der Mikrostruktur für jede Verarbeitungsaktivität von wesentlicher Bedeutung ist, wird in dieser Dissertation ein Phasenfeldmodell mit Flüssigphasenkonvektion verwendet, in dem die Wechselwirkung von diffusiv-konvektiven Feldern und deren Auswirkung auf die Gefügeentwicklung untersucht wird. Im folgenden Teil werden die numerischen Ergebnisse unter einem diffusionskonvektiven Regime von den Korngrenzen bis zu den Säulendendriten diskutiert. Zunächst wird ein Phasenfeldmodell verwendet, um das Phänomen des Korngrenzenrillens unter Gleichgewichtsbedingungen zu untersuchen. Das Modell wird validiert, indem die Rillenkinetik mit der volumendiffusionsgesteuerten Rillentheorie verglichen wird. In Form der Schmelzkonvektion wird erstmals die Rolle eines zusätzlichen konvektiven Transportmechanismus auf Korngrenzenrillen eingehend untersucht. Die simulierten Rillen zeigen eine hervorragende Übereinstimmung mit früheren experimentellen Theorien sowie mit der Theorie der scharfen Grenzflächen. Daneben wird auch die Wanderung der Fest-Fest-Korngrenze erfasst, wobei das Auftreten asymmetrischer Grate die seitliche Drift der Rillenwurzel entlang der stromabwärtigen Richtung fördert. Darüber hinaus wird die Initiierung von Mikrostrukturmustern für energetisch isotrope Grenzflächen vorgestellt, wobei die Vorhersage der Spitzenaufteilungsposition anhand eines analytischen Kriteriums diskutiert wird. Infolge von krümmungsgetriebenen Flüssen wird die fundamentale und sich wiederholende Einheit von Mikrostrukturen mit Spitzenspaltung durch einen direkten Vergleich zwischen dem Phasenfeld und der Position der scharfen Grenzflächenspitze analysiert. Im Gegensatz zu den vorhandenen Studien sagt das vorgeschlagene Kriterium die Verzweigungsposition in einem erstarrenden Muster erfolgreich voraus. Anschließend wird der Einfluss anderer Parameter wie der Grenzflächenanisotropie, der Schmelzkonvektion und der Oberflächenenergien auf den strukturellen Übergang von Mikrostrukturen mit Spitzenspaltung ermittelt. Während für ein isotropes Kristallwachstum eine Morphologie der Spitzenaufspaltung beobachtet wird, wird für anisotrope Grenzflächen das Auftreten von richtungsabhängigen säulenförmigen Dendriten demonstriert. Anschließend wird die Vorhersage des interdendritischen Armabstands bei vorhandener Schmelzkonvektion untersucht. In Übereinstimmung mit früheren experimentellen Studien wird gezeigt, dass der Selektionsmechanismus von Primärarmen durch das Eintauchen von Dendriten in das Diffusionsregime zum Überwachsen von Tertiärarmen im Diffusionskonvektionsregime führt. Darüber hinaus zeigt sich, dass die Vorhersage des primä}ren Dendritenarmabstands aufgrund des Vorhandenseins eines konvektiven Transports im interdendritischen Bereich modifiziert ist. Danach werden Phasenfeldsimulationen durchgeführt, um die Wachstumskonkurrenz von Säulendendriten vorherzusagen, die an der Korngrenze konvergieren. Während der Herstellung von Einkristall-Turbinenschaufeln häufig untersucht, wird das Überwuchsverhalten von falsch ausgerichteten Dendriten an der Korngrenze erfasst und analysiert. Zum ersten Mal wird gezeigt, dass das Vorhandensein eines zusätzlichen Massentransports in der flüssigen Massenphase die gelösten dendritischen Spitzen fördert, was wiederum denÜberwuchsmechanismus an der Korngrenze modifiziert. Durch mikrostrukturelle Auswahlkarten wird auch gezeigt, dass Parameter wie der Fehlorientierungswinkel und die Grenzflächenanisotropie dieÜberwuchsdynamik an der Korngrenze weitgehend steuern

Random Quantum Circuits

Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as new dynamical phases in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.Comment: Review article for Annual Review of Condensed Matter Physics; comments welcom

Towards local tracking of solvated metal ions at solid-liquid interfaces

The dynamics of individual solvated ions near solid surfaces is the driving force behind numerous interfacial processes, from electrochemical reactions to charge storage, mineral growth, biosignalling and bioenergetics. The precise system behaviour is delicately dependent on the atomistic and molecular details of the interface and remains difficult to capture with generalisable, analytical models. Reported dynamics can vary by orders of magnitude depending on microscopic details of the solvent, ions and/or surface chemistry. Experimentally, tracking single solvated ions as they move at or along interfaces remains highly challenging. This is, to some extent, offset by simulations that can provide precise atomistic insights, but usually over limited timescales. The aim of this review is to provide an overview of this highly interdisciplinary field, its achievements and remaining challenges, reviewing both experimental and computational results. Starting from the well accepted continuum description of dissolved ions at solid-liquid interfaces, we outline the challenges of deriving local information, illustrating the discussion with a range of selected studies. We explore the challenges associated with simultaneously achieving the spatial and temporal resolution needed to gain meaningful, yet contextual insights of single ions’ dynamics. Based on the current studies, we anticipate the future developments in the field, outlining remaining challenges and opportunities

On the critical nature of plastic flow: one and two dimensional models

Steady state plastic flows have been compared to developed turbulence because the two phenomena share the inherent complexity of particle trajectories, the scale free spatial patterns and the power law statistics of fluctuations. The origin of the apparently chaotic and at the same time highly correlated microscopic response in plasticity remains hidden behind conventional engineering models which are based on smooth fitting functions. To regain access to fluctuations, we study in this paper a minimal mesoscopic model whose goal is to elucidate the origin of scale free behavior in plasticity. We limit our description to fcc type crystals and leave out both temperature and rate effects. We provide simple illustrations of the fact that complexity in rate independent athermal plastic flows is due to marginal stability of the underlying elastic system. Our conclusions are based on a reduction of an over-damped visco-elasticity problem for a system with a rugged elastic energy landscape to an integer valued automaton. We start with an overdamped one dimensional model and show that it reproduces the main macroscopic phenomenology of rate independent plastic behavior but falls short of generating self similar structure of fluctuations. We then provide evidence that a two dimensional model is already adequate for describing power law statistics of avalanches and fractal character of dislocation patterning. In addition to capturing experimentally measured critical exponents, the proposed minimal model shows finite size scaling collapse and generates realistic shape functions in the scaling laws.Comment: 72 pages, 40 Figures, International Journal of Engineering Science for the special issue in honor of Victor Berdichevsky, 201

Cascades and transitions in turbulent flows

Turbulence is characterized by the non-linear cascades of energy and other inviscid invariants across a huge range of scales, from where they are injected to where they are dissipated. Recently, new experimental, numerical and theoretical works have revealed that many turbulent configurations deviate from the ideal 3D/2D isotropic cases characterized by the presence of a strictly direct/inverse energy cascade, respectively. We review recent works from a unified point of view and we present a classification of all known transfer mechanisms. Beside the classical cases of direct and inverse cascades, the different scenarios include: split cascades to small and large scales simultaneously, multiple/dual cascades of different quantities, bi-directional cascades where direct and inverse transfers of the same invariant coexist in the same scale-range and finally equilibrium states where no cascades are present, including the case when a condensate is formed. We classify all transitions as the control parameters are changed and we analyse when and why different configurations are observed. Our discussion is based on a set of paradigmatic applications: helical turbulence, rotating and/or stratified flows, MHD and passive/active scalars where the transfer properties are altered as one changes the embedding dimensions, the thickness of the domain or other relevant control parameters, as the Reynolds, Rossby, Froude, Peclet, or Alfven numbers. We discuss the presence of anomalous scaling laws in connection with the intermittent nature of the energy dissipation in configuration space. An overview is also provided concerning cascades in other applications such as bounded flows, quantum, relativistic and compressible turbulence, and active matter, together with implications for turbulent modelling. Finally, we present a series of open problems and challenges that future work needs to address.Comment: accepted for publication on Physics Reports 201

Exploring spacetime phenomenology: from Lorentz violations to experimental tests of non-locality

This thesis deals primarily with the phenomenology associated to quantum aspects of spacetime. In particular, it aims at exploring the phenomenological consequences of a fundamental discreteness of the spacetime fabric, as predicted by several quantum gravity models and strongly hinted by many theoretical insights. The first part of this work considers a toy-model of emergent spacetime in the context of analogue gravity. The way in which a relativistic Bose\u2013 Einstein condensate can mimic, under specific configurations, the dynamics of a scalar theory of gravity will be investigated. This constitutes proof-ofconcept that a legitimate dynamical Lorentzian spacetime may emerge from non-gravitational (discrete) degrees of freedom. Remarkably, this model will emphasize the fact that in general, even when arising from a relativistic system, any emergent spacetime is prone to show deviations from exact Lorentz invariance. This will lead us to consider Lorentz Invariance Violations as first candidate for a discrete spacetime phenomenology. Having reviewed the current constraints on Lorentz Violations and studied in depth viable resolutions of their apparent naturalness problem, the second part of this thesis focusses on models based on Lorentz invariance. In the context of Casual Set theory, the coexistence of Lorentz invariance and discreteness leads to an inherently nonlocal scalar field theory over causal sets well approximating a continuum spacetime. The quantum aspects of the theory in flat spacetime will be studied and the consequences of its non-locality will be spelled out. Noticeably, these studies will lend support to a possible dimensional reduction at small scales and, in a classical setting, show that the scalar field is characterized by a universal nonminimal coupling when considered in curved spacetimes. Finally, the phenomenological possibilities for detecting this non-locality will be investigated. First, by considering the related spontaneous emission of particle detectors, then by developing a phenomenological model to test nonlocal effects using opto-mechanical, non-relativistic systems. In both cases, one could be able to cast in the near future stringent bounds on the non-locality scale