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"This thesis presents an accurate and advanced numerical methodology to remedy difficulties such as direct numerical simulation of magnetohydrodynamic (MHD) flow in computational fluid dynamics (CFD), grid generation processes in tokamak fusion facilities, and the coupling between the surface tension force and Lorentz force in the metallurgical industry. In addition, on the basis of the numerical platform it establishes, it also investigates selected interesting topics, e.g. single bubble motion under the influence of either vertical or horizontal magnetic fields. Furthermore, it confirms the relation between the bubble’s path instability and wake instability, and observes the anisotropic (isotropic) effect of the vertical (horizontal) magnetic field on the vortex structures, which determines the dynamic behavior of the rising bubble.The direct numerical simulation of magnetohydrodynamic (MHD) flows has proven difficult in the field of computational fluid dynamic (CFD) research, because it not only concerns the coupling of the equations governing the electromagnetic field and the fluid motion, but also calls for suitable numerical methods for computing the electromagnetic field. In tokamak fusion facilities, where the MHD effect is significant and the flow domain is complex, the process of grid generation requires considerable time and effort. Moreover, in the metallurgical industry, where multiphase MHD flows are usually encountered, the coupling between the surface tension force and Lorentz force adds to the difficulty of deriving direct numerical simulations."

"This book is the most comprehensive review of high-resolution schemes based on the principle of Flux-Corrected Transport (FCT). Book describe the development of the classical FCT methodology for convection-dominated transport problems, while the design philosophy behind modern FCT schemes is explained by S.T. Zalesak. The subsequent chapters present various improvements and generalizations proposed over the past three decades. In this new edition, recent results are integrated into existing chapters in order to describe significant advances since the publication of the first edition. Also, 3 new chapters were added in order to cover the following topics, algebraic flux correction for finite elements, iterative and linearized FCT schemes, TVD-like flux limiters, acceleration of explicit and implicit solvers, mesh adaptation, failsafe limiting for systems of conservation laws, flux-corrected interpolation (remapping), positivity preservation in RANS turbulence models, and the use of FCT as an implicit subgrid scale model for large eddy simulations."

"Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field. "

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Computational Fluid Dynamics (CFD) merupakan metode analisis numerik aliran fluida, perpidahan panas, dan fenomena terkait. Simulasi CFD seringkali membutuhkan waktu yang lama dan biaya komputasi yang mahal. Ini disebabkan oleh kompleksitas persamaan atur yang mendasari perilaku aliran. Dewasa ini, Model berbasis data (Data driven model) telah mendorong perkembangan pada banyak disiplin sains dan teknik, termasuk CFD. Melalui model berbasis data, orde dari persamaan atur dapat direduksi sehingga menghasilkan reduced order model (ROM). Penelitian ini bertujuan untuk menjelaskan algoritma dasar ROM untuk menyelesaikan kasus aliran menggunakan library ITHACA-FV. Kasus aliran fluida yang menjadi domain adalah aliran stedi tak mampu mampat Navier-Stokes pada backward-facing step. Kemudian solusi FOM dan ROM dibandingkan. Pada simulasi ROM mode 1 pada kasus backward-facing step terdapat error rata-rata sebesar 2,730% untuk data kecepatan dan 0,113% untuk data tekanan. Sedangkan simulasi ROM mode 3 pada kasus yang sama memiliki error rata-rata 1,085% untuk data kecepatan dan 0,058% untuk data tekanan.

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Computational Fluid Dynamics (CFD) is a method of numerical analysis of fluid flow, heat transfer, and related phenomena. CFD simulation often takes a long time and is computationally expensive. This is due to the complexity of the governing equations that underlie flow behavior. Fluid flow is governed by the Navier-Stokes equation which is non-linear and generally produces a random behavior called turbulence. Today, Data driven models have made developments in many scientific and engineering disciplines, including CFD. Through a data-based model, the order of the governing equations can be reduced to produce a reduced order model (ROM). This study aims to explain the basic ROM algorithm to solve fluid flow cases through the ITHACA-FV library. The fluid flow case that becomes the domain is the steady-state Navier-Stokes incompressible flow in the backward-facing step. Then the FOM and ROM solutions are compared. ROM mode 1 simulation has average error of 2.730% for velocity and 0.113% for pressure data. ROM mode 3 simulation has an average error of 1.085% for speed data and 0.058% for pressure data.

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"Flow control and optimization has been an important part of experimental flow science throughout the last century. As research in computational fluid dynamics (CFD) matured, CFD codes were routinely used for the simulation of fluid flows. Subsequently, mathematicians and engineers began examining the use of CFD algorithms and codes for optimization and control problems for fluid flows. The marriage of mature CFD methodologies with state-of-the-art optimization methods has become the center of activity in computational flow control and optimization.Perspectives in Flow Control and Optimization presents flow control and optimization as a subdiscipline of computational mathematics and computational engineering. It introduces the development and analysis of several approaches for solving flow control and optimization problems through the use of modern CFD and optimization methods. The author discusses many of the issues that arise in the practical implementation of algorithms for flow control and optimization, such as choices to be made and difficulties to overcome. He provides the reader with a clear idea of what types of flow control and optimization problems can be solved, how to develop effective algorithms for solving such problems, and potential problems to be aware of when implementing the algorithms.This book is written for both those new to the field of control and optimization as well as experienced practitioners, including engineers, applied mathematicians, and scientists interested in computational methods for flow control and optimization. Both those interested in developing new algorithms and those interested in the application of existing algorithms should find useful information in this book."

"This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.An expanded treatment of Gaussian elimination incorporates rook pivoting, along with a thorough discussion of the choice of pivoting strategy and the effects of scaling. The book's detailed descriptions of floating point arithmetic and of software issues reflect the fact that IEEE arithmetic is now ubiquitous.Although not designed specifically as a textbook, this new edition is a suitable reference for an advanced course. It can also be used by instructors at all levels as a supplementary text from which to draw examples, historical perspective, statements of results, and exercises. With its thorough indexes and extensive, up-to-date bibliography, the book provides a mine of information in a readily accessible form."

"This book treats the numerical analysis of finite element computational fluid dynamics. Assuming minimal background, the text covers finite element methods; the derivation, behavior, analysis, and numerical analysis of Navier-tokes equations; and turbulence and turbulence models used in simulations. Each chapter on theory is followed by a numerical analysis chapter that expands on the theory. The chapters contain numerous exercises."

"Memetic Algorithms (MAs) are computational intelligence structures combining multiple and various operators in order to address optimization problems. The combination and interaction amongst operators evolves and promotes the diffusion of the most successful units and generates an algorithmic behavior which can handle complex objective functions and hard fitness landscapes. “Handbook of memetic algorithms” organizes, in a structured way, all the the most important results in the field of MAs since their earliest definition until now. A broad review including various algorithmic solutions as well as successful applications is included in this book. Each class of optimization problems, such as constrained optimization, multi-objective optimization, continuous vs combinatorial problems, uncertainties, are analysed separately and, for each problem, memetic recipes for tackling the difficulties are given with some successful examples. "

"This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems."