1,720,968 research outputs found
Dynamic Capillarity and Hysteretic Effects in TwoPhase Flow in Porous Media: Modeling, Upscaling and Simulation
No full textFlow and transport processes in porous media are relevant for a huge variety of applications covering all areas of modern society. To describe and predict the relevant processes, it is crucial to understand the complicated underlying phenomena. The mathematical models are based on fundamental balance equations, which are complemented by constitutive equations describing the specific material behavior. These relations must be expressed using effective parameters, which should combine all porescale effects.
However, these parameters are simply postulated in many state-of-the-art models and not derived from a pore-scale model. In particular, the interface dynamics between the fluids are typically neglected or incorporated on an empirical basis. In the first part of this work, we consider these effects for simple pore geometries and apply upscaling techniques to derive effective two-phase flow equations.
The upscaled models at the Darcy scale are coupled, nonlinear partial differential equations, which may even degenerate and can involve strong heterogeneities or even discontinuous physical properties. These issues raise analytical and numerical challenges. Besides appropriate discretization methods, linearization schemes must be applied. By domain decomposition methods, essentially different regions are decoupled to parallelize computations and reach a reasonable performance. These numerical aspects are considered in the second part of this work
Dynamic Capillarity and Hysteretic Effects in TwoPhase Flow in Porous Media: Modeling, Upscaling and Simulation
No full textFlow and transport processes in porous media are relevant for a huge variety of applications covering all areas of modern society. To describe and predict the relevant processes, it is crucial to understand the complicated underlying phenomena. The mathematical models are based on fundamental balance equations, which are complemented by constitutive equations describing the specific material behavior. These relations must be expressed using effective parameters, which should combine all porescale effects.
However, these parameters are simply postulated in many state-of-the-art models and not derived from a pore-scale model. In particular, the interface dynamics between the fluids are typically neglected or incorporated on an empirical basis. In the first part of this work, we consider these effects for simple pore geometries and apply upscaling techniques to derive effective two-phase flow equations.
The upscaled models at the Darcy scale are coupled, nonlinear partial differential equations, which may even degenerate and can involve strong heterogeneities or even discontinuous physical properties. These issues raise analytical and numerical challenges. Besides appropriate discretization methods, linearization schemes must be applied. By domain decomposition methods, essentially different regions are decoupled to parallelize computations and reach a reasonable performance. These numerical aspects are considered in the second part of this work
Non-Overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations
No full textNonlinear advection-diffusion equations often arise in the modeling of transport processes. We propose for these equations a non-overlapping domain decomposition algorithm of Schwarz waveform-relaxation (SWR) type. It relies on nonlinear zeroth-order (or Robin) transmission conditions between the sub-domains that ensure the continuity of the converged solution and of its normal flux across the interface. We prove existence of unique iterative solutions and the convergence of the algorithm. We then present a numerical discretization for solving the SWR problems using a forward Euler discretization in time and a finite volume method in space, including a local Newton iteration for solving the nonlinear transmission conditions. Our discrete algorithm is asymptotic preserving, i.e., robust in the vanishing viscosity limit. Finally, we present numerical results that confirm the theoretical findings, in particular the convergence of the algorithm. Moreover, we show that the SWR algorithm can be successfully applied to two-phase flow problems in porous media as paradigms for evolution equations with strongly nonlinear advective and diffusive fluxes. 1. Introduction. Nonlinear advection-diffusion equations often arise in the mod-eling of transport processes, especially in porous media. Typical examples are (en-hanced) oil recovery, CO 2 storage, and geothermal energy production. Since measurements of such processes are usually impossible or at best very difficult and thus very rare, numerical simulations are essential for an adequate understanding. The precise formulation of the underlying nonlinear advection-diffusion equations can involve strong heterogeneities due to largely varying physical properties and parameters. In turn, this raises significant mathematical and computational problems, such that the development and analysis of robust discretization methods becomes a non-trivial challenge. To still reach reasonable performance, a typical approach is the parallelization by a domain decomposition method, which is an established technique for steady problems; see [11, 45, 50, 52] and references therein. Regardless of the chosen dis-cretization method and of the linearization scheme, these methods aim at reducing th
Consistent and Asymptotic-Preserving Finite-Volume Domain Decomposition Methods for Singularly Perturbed Elliptic Equations
No full textLinearized domain decomposition methods for two-phase porous media flow models involving dynamic capillarity and hysteresis
Full text linkWe discuss two linearization and domain decomposition methods for mathematical models for two-phase flow in a porous medium. The medium consists of two adjacent regions with possibly different parameterizations. The model accounts for non-equilibrium effects like dynamic capillarity and hysteresis. The θ-scheme is adopted for the temporal discretization of the equations yielding nonlinear time-discrete equations. For these, we propose and analyze two iterative schemes, which combine a stabilized linearization iteration of fixed-point type, the L-scheme, and a non-overlapping domain decomposition method into one iteration. First, we prove the existence of unique solutions to the problems defining the linear iterations. Then, we give the rigorous convergence proof for both iterative schemes towards the solution of the time-discrete equations. The developed schemes are independent of the spatial discretization or the mesh and avoid the use of derivatives as in Newton based iterations. Their convergence holds independently of the initial guess, and under mild constraints on the time step. The numerical examples confirm the theoretical results and demonstrate the robustness of the schemes. In particular, the second scheme is well suited for models incorporating hysteresis. The schemes can be easily implemented for realistic applications
On an averaged model for immiscible two‐phase flow with surface tension and dynamic contact angle in a thin strip
No full textWe consider a model for the flow of two immiscible fluids in a two-dimensional thin strip of varying width. This represents an idealization of a pore in a porous medium. The interface separating the fluids forms a freely moving interface in contact with the wall and is driven by the fluid flow and surface tension. The contact-line model incorporates Navier-slip boundary conditions and a dynamic and possibly hysteretic contact angle law. We assume a scale separation between the typical width and the length of the thin strip. Based on asymptotic expansions, we derive effective models for the two-phase flow. These models form a system of differential algebraic equations for the interface position and the total flux. The result is Darcy-type equations for the flow, combined with a capillary pressure-saturation relationship involving dynamic effects. Finally, we provide some numerical examples to show the effect of a varying wall width, of the viscosity ratio, of the slip boundary condition as well as of having a dynamic contact angle law.Universiteit Hasselt, Grant/Award Number: BOF17NI01; Deutsche Forschungsgemeinschaft, Grant/Award Number: 327154368; FondsWetenschappelijk Onderzoek, Grant/Award Numbers: G051418N, G0G1316
Dynamic effects during the capillary rise of fluids in cylindrical tubes
Full text linkThe mathematical models for the capillary-driven flow of fluids in tubes typically assume a static contact angle at the fluid–air contact line on the tube walls. However, the dynamic evolution of the fluid–air interface is an important feature during capillary rise. Furthermore, inertial effects are relevant at early times and may lead to oscillations. To incorporate and quantify the different effects, a fundamental description of the physical processes within the tube is used to derive an upscaled model of capillary-driven flow in circular cylindrical tubes. The upscaled model extends the classical Lucas–Washburn model by incorporating a dynamic contact angle and slip. It is then further extended to account for inertial effects. Finally, the solutions of the different models are compared to experimental data. In contrast to the Lucas–Washburn model, the models with dynamic contact angle match well the experimental data, both the rise height and the contact angle, even at early times. The models have a free parameter through the dynamic contact angle description, which is fitted using the experimental data. The findings here suggest that this parameter depends only on the properties of the fluid but is independent of geometrical features, such as the tube radius. Therefore, the presented models can predict the capillary-driven flow in tubular systems upon knowledge of the underlying dynamic contact-angle relation
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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