Download or read book Multiscale Model Reduction for Unsteady Fluid Flow written by Jared Callaham and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation develops methods for constructing simplified models of unsteady fluid flows in regimes ranging from weakly nonlinear to fully turbulent. These models can provide valuable insights into the flow physics, as well as inexpensive surrogate models suitable for analytic study and controller design. The emphasis is on extending traditional methods using recent advances in data-driven modeling in a manner that preserves the interpretability and robustness of classical analysis. Throughout, the proposed methodological developments are critically evaluated against extensive computational fluid dynamics simulations and experimental wind tunnel observations representing a variety of fundamental features of unsteady flows. This work takes three distinct approaches to model reduction. First, a perspective of the fluid flow as a high-dimensional, dissipative dynamical system with emergent large-scale coherence leads to approximations in terms of low-dimensional nonlinear dynamics. These models can be derived by projection of the governing equations or sparse model discovery; in either case it is crucial to systematically account for the influence of unresolved degrees of freedom. Alternatively, in fully-developed turbulence the evolution of global integral quantities can be viewed as deterministic motion forced by incoherent fluctuations. The analogy with statistical mechanics cannot be made rigorous for turbulence, but an empirical method is developed to approximate these generalized Brownian motions from limited experimental data. Finally, the observation that the behavior of physical systems is often determined by a dominant balance between a small subset of physical mechanisms motivates the development of an algorithm for objective identification of regions with different active physics. Underlying all of these frameworks is a unifying perspective of the flow as a system with complex nonlinear interactions across a wide range of spatiotemporal scales.

Download or read book Reduced Order Methods for Modeling and Computational Reduction written by Alfio Quarteroni and published by Springer. This book was released on 2014-06-05 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

Download or read book Generalized Discontinuous Multiscale Methods for Flows in Highly Heterogeneous Porous Media written by Minam Moon and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is devoted to the development, study and testing of numerical methods for elliptic and parabolic equations with heterogeneous coefficients. The motivation for this study is to meet the need for fast and robust methods for numerical upscaling and simulation of single and multi-phase fluid flow in highly heterogeneous porous media. We consider the multiscale model reduction technique in the framework of the discontinuous Galerkin (DG) and the hybridizable discontinuous Galerkin (HDG) finite element methods. First, we design multiscale finite element methods for second order elliptic equations by applying the symmetric interior penalty discontinuous Galekin finite element method. We propose two different types of finite element spaces on the coarse mesh within DG framework. The first type of spaces is based on a local spectral problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the mass matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. Second, we develop multiscale model reduction methods within the HDG framework. We provide construction of several multiscale finite element spaces (related to the coarse-mesh edges) that guarantee a reasonable approximation on a reduced dimensional space of the numerical traces. In these approaches, we use local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We also provide a general framework for systematic construction of multiscale spaces. By using local snapshots we were able to add local features to the solution space and to avoid high dimensional representation of trace spaces. Further, we extend multiscale finite element methods within HDG method to nonlinear and/or time-dependent problems. These extensions demonstrate the potential of the proposed constructions for some advanced and more practical applications. For most of the proposed methods, we investigate their stability and derive error estimates for the approximate solutions. Furthermore we study the performance of all proposed methods on a representative number of numerical examples. In the numerical tests, we use various permeability data of highly heterogeneous porous media and contrasts ranging from 103 to 106. Since the exact solution is in general unknown, we first generate solutions on a very fine mesh and use them as reference solutions in our tests. The numerical results confirm the theoretical study of the accuracy of the proposed methods and their robustness with respect to the media contrast. Our numerical experiments also show that the proposed methods could be implemented in a practical and efficient way. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155430

Download or read book Multiscale Model Reduction for High contrast Flow Problems written by Guanglian Li and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Many applications involve media that contain multiple scales and physical properties that vary in orders of magnitude. One example is a rock sample, which has many micro-scale features. Most multiscale problems are often parameter-dependent, where the parameters represent variations in medium properties, randomness, or spatial heterogeneities. Because of disparity of scales in multiscale problems, solving such problems is prohibitively expensive. Among the most popular and developed techniques for efficiently solving the global system arising from a finite element approximation of the underlying problem on a very fine mesh are multigrid methods, multilevel methods, and domain decomposition techniques. More recently, a new large class of accurate reduced-order methods has been introduced and used in various applications. These include Galerkin multiscale finite element methods, mixed multiscale finite element methods, multiscale finite volume methods, and mortar multiscale methods, and so on. In this dissertation, a multiscale finite element method is studied for the computation of heterogeneous problems involving high-contrast, no-scale separation, parameter dependency and nonlinearities. A general formulation of the elliptic heterogeneous problems is discussed, including an oversampling strategy and randomized snapshots generation for a more efficient and accurate computation. Furthermore, a multiscale adaptive algorithm is proposed and analyzed to reduce the computational cost. Then, this multiscale finite element method is extended to the nonlinear high-contrast elliptic problems. Specifically, both continuous and discontinuous Galerkin formulations are considered. In the end, an application to high-contrast heterogeneous Brinkman flow is analyzed. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155073

Download or read book Model Reduction of Parametrized Systems written by Peter Benner and published by Springer. This book was released on 2017-09-05 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

Download or read book Data driven modeling and optimization in fluid dynamics From physics based to machine learning approaches written by Michel Bergmann and published by Frontiers Media SA. This book was released on 2023-01-05 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multiscale Multibody Dynamics written by Jielong Wang and published by Springer Nature. This book was released on 2023-03-24 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel theory of multibody dynamics with distinct features, including unified continuum theory, multiscale modeling technology of multibody system, and motion formalism implementation. All these features together with the introductions of fundamental concepts of vector, dual vector, tensor, dual tensor, recursive descriptions of joints, and the higher-order implicit solvers formulate the scope of the book’s content. In this book, a multibody system is defined as a set consisted of flexible and rigid bodies which are connected by any kinds of joints or constraints to achieve the desired motion. Generally, the motion of multibody system includes the translation and rotation; it is more efficient to describe the motion by using the dual vector or dual tensor directly instead of defining two types of variables, the translation and rotation separately. Furthermore, this book addresses the detail of motion formalism and its finite element implementation of the solid, shell-like, and beam-like structures. It also introduces the fundamental concepts of mechanics, such as the definition of vector, dual vector, tensor, and dual tensor, briefly. Without following the Einstein summation convention, the first- and second-order tensor operations in this book are depicted by linear algebraic operation symbols of row array, column array, and two-dimensional matrix, making these operations easier to understand. In addition, for the integral of governing equations of motion, a set of ordinary differential equations for the finite element-based discrete system, the book discussed the implementation of implicit solvers in detail and introduced the well-developed RADAU IIA algorithms based on post-error estimation to make the contents of the book complete. The intended readers of this book are senior engineers and graduate students in related engineering fields.

Download or read book Certified Reduced Basis Methods for Parametrized Partial Differential Equations written by Jan S Hesthaven and published by Springer. This book was released on 2015-08-20 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

Download or read book Control and Optimization of Multiscale Process Systems written by Panagiotis D. Christofides and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book—the first of its kind—presents general methods for feedback controller synthesis and optimization of multiscale systems, illustrating their application to thin-film growth, sputtering processes, and catalytic systems of industrial interest. The authors demonstrate the advantages of the methods presented for control and optimization through extensive simulations. Included in the work are new techniques for feedback controller design and optimization of multiscale process systems that are not included in other books. The book also contains a rich collection of new research topics and references to significant recent work.

Download or read book Recent Numerical Advances in Fluid Mechanics written by Omer San and published by MDPI. This book was released on 2020-07-03 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent decades, the field of computational fluid dynamics has made significant advances in enabling advanced computing architectures to understand many phenomena in biological, geophysical, and engineering fluid flows. Almost all research areas in fluids use numerical methods at various complexities: from molecular to continuum descriptions; from laminar to turbulent regimes; from low speed to hypersonic, from stencil-based computations to meshless approaches; from local basis functions to global expansions, as well as from first-order approximation to high-order with spectral accuracy. Many successful efforts have been put forth in dynamic adaptation strategies, e.g., adaptive mesh refinement and multiresolution representation approaches. Furthermore, with recent advances in artificial intelligence and heterogeneous computing, the broader fluids community has gained the momentum to revisit and investigate such practices. This Special Issue, containing a collection of 13 papers, brings together researchers to address recent numerical advances in fluid mechanics.

Download or read book Projection based Model Order Reduction and Hyperreduction of Turbulent Flow Models written by Sebastian Johannes Grimberg and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite significant advances in simulation-based engineering science in recent decades, time-critical applications struggle to take advantage of high-fidelity, partial differential equation-based computer simulation. This is due to the large processing time and storage requirements associated with large-scale computational models. Projection-based model order reduction (PMOR) methods offer the ability to dramatically reduce this computational cost by generating compact, low-dimensional models for which solutions can be obtained in near real-time while still retaining the accuracy of an associated high-fidelity, high-dimensional model for the time and parameter domain of interest. PMOR is thus an essential technology for the application of model-based control, probabilistic analysis, or design optimization to problems involving increasingly complex engineered systems and physical phenomena. Unfortunately, nonlinear problems, in particular turbulent computational fluid dynamics (CFD) applications, continue to present a number of challenges for constructing stable, accurate, and computationally efficient projection-based reduced order models (PROMs). This thesis addresses some of these challenges, demonstrating PROMs for a number of large-scale, unsteady, turbulent flow applications which showcase the potential of PMOR for nonlinear CFD models with multiscale physics. These results leverage advancements in hyperreduction, a technique for the treatment of nonlinearities in the underlying computational model, to obtain CPU time and wall-clock time speedup factors of several orders of magnitude. This work also presents an investigation of the role of projection in the numerical stability of PMOR for convection-dominated flow problems, ultimately disproving an often-stated claim in the literature with the support of several numerical examples.

Download or read book Reduction Approximation Machine Learning Surrogates Emulators and Simulators written by Gianluigi Rozza and published by Springer Nature. This book was released on with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Principles of Multiscale Modeling written by Weinan E and published by Cambridge University Press. This book was released on 2011-07-07 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic discussion of the fundamental principles, written by a leading contributor to the field.

Download or read book DEVELOPMENT OF AN ADAPTIVE MULTISCALE NONLINEAR DISTURBANCE EQUATIONS SOLVER written by Amandeep Premi and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the development of an incompressible, adaptive, multiscale, nonlinear disturbance equations solver in the finite-volume OpenFOAM(v4.1) framework. The nonlinear disturbance equations are derived from the Navier-Stokes equations by representing the primary flow variables as a sum of steady and time-varying components and then subtracting the steady flow Navier-Stokes equations out of the resulting equations. The application of these equations to resolve the unsteady behavior of a fluid flow offers opportunities to save on substantial amounts of computational effort. These savings are made possible by reduction in the amount of spatial and temporal discretization that is required to solve the problem. However, these savings are only practical when certain conditions are met, which can vary based on the problem at hand. To encompass the domain of problems, where these savings are plausible, a generalized formulation of the nonlinear disturbance equations in terms of the equation formulation and numerical solution procedure is essential. In this work, the nonlinear disturbance equations are implemented in an incompressible format with both block-coupled as well as segregated solution strategies using collocated, finite-volume grids. A novel disturbance-pressure and disturbance-velocity coupling scheme is also developed for the segregated solver. The developed solver features multiscale capabilities with the addition of wavelet-based runtime analysis. The wavelet analysis is restricted to a predefined number of scales to keep the computational-stencil small and local. This allows the analysis to be computationally inexpensive and compatible with finite-volume computational fluid dynamics (CFD) solvers. The multiscale architecture is utilized to enable adaptive mesh refinement with a physics-based adaptable large eddy simulation (LES) type filter. The multiscale capabilities are also explored for detection of changes in the flow behavior, like the transition of the flow from laminar to turbulent. The application of the developed solver in the areas of laminar-flow stability and gust modeling is also explored.This solver aims to implement a generalized form of incompressible nonlinear disturbance equations in both coupled/segregated form with adaptive multiresolution capabilities in an open-source finite-volume framework. This makes the current work a novel advancement in terms of concept and applicability. The generalized formulation makes it applicable to many unsteady-aerodynamics problems and the finite-volume framework with segregated solver makes it practical to apply it to real-world problems with variety of options for numerical solvers.

Download or read book Model Reduction and Approximation written by Peter Benner and published by SIAM. This book was released on 2017-07-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.

Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Download or read book Reduced Basis Methods for Partial Differential Equations written by Alfio Quarteroni and published by Springer. This book was released on 2015-08-19 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit