101 research outputs found

    Non-Local Multi-Continuum method (NLMC) for Darcy-Forchheimer flow in fractured media

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    This work presents the application of the non-local multicontinuum method (NLMC) for the Darcy-Forchheimer model in fractured media. The mathematical model describes a nonlinear flow in fractured porous media with a high inertial effect and flow speed. The space approximation is constructed on the sufficiently fine grid using a finite volume method (FVM) with an embedded fracture model (EFM) to approximate lower dimensional fractures. A non-local model reduction approach is presented based on localization and constraint energy minimization. The multiscale basis functions are constructed in oversampled local domains to consider the flow effects from neighboring local domains. Numerical results are presented for a two-dimensional formulation with two test cases of heterogeneity. The influence of model nonlinearity on the multiscale method accuracy is investigated. The numerical results show that the non-local multicontinuum method provides highly accurate results for Darcy-Forchheimer flow in fractured media

    Lattice Boltzmann Methods for Partial Differential Equations

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    Lattice Boltzmann methods provide a robust and highly scalable numerical technique in modern computational fluid dynamics. Besides the discretization procedure, the relaxation principles form the basis of any lattice Boltzmann scheme and render the method a bottom-up approach, which obstructs its development for approximating broad classes of partial differential equations. This work introduces a novel coherent mathematical path to jointly approach the topics of constructability, stability, and limit consistency for lattice Boltzmann methods. A new constructive ansatz for lattice Boltzmann equations is introduced, which highlights the concept of relaxation in a top-down procedure starting at the targeted partial differential equation. Modular convergence proofs are used at each step to identify the key ingredients of relaxation frequencies, equilibria, and moment bases in the ansatz, which determine linear and nonlinear stability as well as consistency orders of relaxation and space-time discretization. For the latter, conventional techniques are employed and extended to determine the impact of the kinetic limit at the very foundation of lattice Boltzmann methods. To computationally analyze nonlinear stability, extensive numerical tests are enabled by combining the intrinsic parallelizability of lattice Boltzmann methods with the platform-agnostic and scalable open-source framework OpenLB. Through upscaling the number and quality of computations, large variations in the parameter spaces of classical benchmark problems are considered for the exploratory indication of methodological insights. Finally, the introduced mathematical and computational techniques are applied for the proposal and analysis of new lattice Boltzmann methods. Based on stabilized relaxation, limit consistent discretizations, and consistent temporal filters, novel numerical schemes are developed for approximating initial value problems and initial boundary value problems as well as coupled systems thereof. In particular, lattice Boltzmann methods are proposed and analyzed for temporal large eddy simulation, for simulating homogenized nonstationary fluid flow through porous media, for binary fluid flow simulations with higher order free energy models, and for the combination with Monte Carlo sampling to approximate statistical solutions of the incompressible Euler equations in three dimensions

    Variational data assimilation for two interface problems

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    “Variational data assimilation (VDA) is a process that uses optimization techniques to determine an initial condition of a dynamical system such that its evolution best fits the observed data. In this dissertation, we develop and analyze the variational data assimilation method with finite element discretization for two interface problems, including the Parabolic Interface equation and the Stokes-Darcy equation with the Beavers-Joseph interface condition. By using Tikhonov regularization and formulating the VDA into an optimization problem, we establish the existence, uniqueness and stability of the optimal solution for each concerned case. Based on weak formulations of the Parabolic Interface equation and Stokes-Darcy equation, the dual method and Lagrange multiplier rule are utilized to derive the first order optimality system (OptS) for both the continuous and discrete VDA problems, where the discrete data assimilations are built on certain finite element discretization in space and the backward Euler scheme in time. By introducing auxiliary equations, rescaling the optimality system, and employing other subtle analysis skills, we present the finite element convergence estimation for each case with special attention paid to recovering the properties missed in between the continuous and discrete OptS. Moreover, to efficiently solve the OptS, we present two classical gradient methods, the steepest descent method and the conjugate gradient method, to reduce the computational cost for well-stabilized and ill-stabilized VDA problems, respectively. Furthermore, we propose the time parallel algorithm and proper orthogonal decomposition method to further optimize the computing efficiency. Finally, numerical results are provided to validate the proposed methods”--Abstract, page iii

    Large Eddy Simulation of Wall-bounded Turbulent Flows at High Reynolds Numbers

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    In the simulation of turbulent flows, resolving flow motions near a solid surface requires a high resolution that is computationally expensive. The present research investigates reducing the computational cost of simulating wall-bounded flows through a technique, called wall-modeling, that introduces the effects of the near-wall flow dynamics as a wall shear stress to the outer layer. Turbulent wall bounded flows were studied using large eddy simulation at moderate to high Reynolds numbers to evaluate the performance of the wall-modeling. The results of wall-modeled turbulent channel flow at Re = 2000 were in good agreement with the experimental data. However, a log-layer mismatch was observed in the mean velocity profile below the matching point due to the inconsistency between the local grid resolution and that required by the subgrid scale model. Moving the matching point further from the wall mitigated the mismatch. The effects of time averaging and temporal filtering schemes on the performance of the wall model were also investigated. It was found that smaller time periods for time averaging result in a wall model that is more responsive to the flow structures in the outer layer. The results indicated that the temporal filtering scheme is strongly dependent on the location of the matching point. Next, the wall-modeling was implemented in the simulation of a turbulent boundary layer. Inflow generation methods were reviewed, and a recycling rescaling method was employed to generate realistic turbulence at the inlet boundary. Zero pressure gradient turbulent boundary layers over a wide range of Reynolds numbers up to Re = 25 523 were studied in terms of the mean velocity profile, Reynolds stress, and skin-friction coefficient. It was found that a wall-modeled turbulent boundary layer can be resolved using a much lower grid resolution in the wall layer. Finally, the wall stress model was implemented to introduce the effects of wall roughness into the wall-modeling via the eddy viscosity. The proposed wall model was examined for transitionally and fully rough channel flows and successful results were achieved. For high-Reynolds number wall-bounded flows, wall-modeling can effectively couple a large eddy simulation to the wall via the wall shear stress without the need to fully resolve the inner region

    New Perspectives in Fluid Dynamics

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    This book contains five chapters detailing significant advances in and applications of new turbulence theory and fluid dynamics modeling with a focus on wave propagation from arbitrary depths to shallow waters, computational modeling for predicting optical distortions through hypersonic flow fields, wind strokes over highway bridges, optimal crop production in a greenhouse, and technological appliance and performance concerns in wheelchair racing. We hope this book to be a useful resource to scientists and engineers who are interested in the fundamentals and applications of fluid dynamics

    Numerical Simulation of Convective-Radiative Heat Transfer

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    This book presents numerical, experimental, and analytical analysis of convective and radiative heat transfer in various engineering and natural systems, including transport phenomena in heat exchangers and furnaces, cooling of electronic heat-generating elements, and thin-film flows in various technical systems. It is well known that such heat transfer mechanisms are dominant in the systems under consideration. Therefore, in-depth study of these regimes is vital for both the growth of industry and the preservation of natural resources. The authors included in this book present insightful and provocative studies on convective and radiative heat transfer using modern analytical techniques. This book will be very useful for academics, engineers, and advanced students

    Numerical Simulation

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    Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students

    Teaching and Learning of Fluid Mechanics

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    This book contains research on the pedagogical aspects of fluid mechanics and includes case studies, lesson plans, articles on historical aspects of fluid mechanics, and novel and interesting experiments and theoretical calculations that convey complex ideas in creative ways. The current volume showcases the teaching practices of fluid dynamicists from different disciplines, ranging from mathematics, physics, mechanical engineering, and environmental engineering to chemical engineering. The suitability of these articles ranges from early undergraduate to graduate level courses and can be read by faculty and students alike. We hope this collection will encourage cross-disciplinary pedagogical practices and give students a glimpse of the wide range of applications of fluid dynamics
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