Download or read book Space time Spectral Collocation Methods for the Magnetohydrodynamics Equations written by Chandramali Piyasundara Wilegoda Liyanage and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods are used to solve partial differential equations numerically. When the solution is analytic, the rate of convergence of the numerical solution is exponential; that is, the error decays exponentially. In time-dependent PDEs, low order finite difference schemes and spectral schemes are traditionally being used for the time and spatial derivatives, respectively. However, applying spectral schemes in both space and time has been thought of recently. These methods have spectral convergence in both spatial and temporal domains. In this thesis, both Chebyshev and Legendre spectral collocation methods are implemented for the Navier-Stokes and Magnetohydrodynamics equations. Numerical solutions for both equations converge exponentially when the solutions are analytic. Moreover, Navier-Stokes and Magnetohydrodynamic equations are implemented for high Reynolds numbers using nonlinear preconditioning methods, ASPIN and RASPEN, which are defined using spectral domain decomposition.

Download or read book Advanced Magnetohydrodynamics written by J. P. Goedbloed and published by Cambridge University Press. This book was released on 2010-04-29 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following on from the companion volume Principles of Magnetohydrodynamics, this textbook analyzes the applications of plasma physics to thermonuclear fusion and plasma astrophysics from the single viewpoint of MHD. This approach turns out to be ever more powerful when applied to streaming plasmas (the vast majority of visible matter in the Universe), toroidal plasmas (the most promising approach to fusion energy), and nonlinear dynamics (where it all comes together with modern computational techniques and extreme transonic and relativistic plasma flows). The textbook interweaves theory and explicit calculations of waves and instabilities of streaming plasmas in complex magnetic geometries. It is ideally suited to advanced undergraduate and graduate courses in plasma physics and astrophysics.

Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Download or read book Magnetohydrodynamics and the Earth s Core written by Andrew M. Soward and published by CRC Press. This book was released on 2002-11-28 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Roberts' research contributions are remarkable in their diversity, depth and international appeal. Papers from the Paul Roberts' Anniversary meeting at the University of Exeter are presented in this volume. Topics include geomagnetism and dynamos, fluid mechanics and MHD, superfluidity, mixed phase regions, mean field electrodynamics and the Earth's inner core. An incisive commentary of the papers puts the work of Paul Roberts into historical context. Magnetohydrodynamics and the Earth's Core provides a valuable source of reference for graduates and researchers working in this area of geoscience.

Download or read book Magnetohydrodynamics of Laboratory and Astrophysical Plasmas written by Hans Goedbloed and published by Cambridge University Press. This book was released on 2019-01-31 with total page 995 pages. Available in PDF, EPUB and Kindle. Book excerpt: With ninety per cent of visible matter in the universe existing in the plasma state, an understanding of magnetohydrodynamics is essential for anyone looking to understand solar and astrophysical processes, from stars to accretion discs and galaxies; as well as laboratory applications focused on harnessing controlled fusion energy. This introduction to magnetohydrodynamics brings together the theory of plasma behavior with advanced topics including the applications of plasma physics to thermonuclear fusion and plasma- astrophysics. Topics covered include streaming and toroidal plasmas, nonlinear dynamics, modern computational techniques, incompressible plasma turbulence and extreme transonic and relativistic plasma flows. The numerical techniques needed to apply magnetohydrodynamics are explained, allowing the reader to move from theory to application and exploit the latest algorithmic advances. Bringing together two previous volumes: Principles of Magnetohydrodynamics and Advanced Magnetohydrodynamics, and completely updated with new examples, insights and applications, this volume constitutes a comprehensive reference for students and researchers interested in plasma physics, astrophysics and thermonuclear fusion.

Download or read book Computational Simulation and Experimental Techniques for Nanofluid Flow written by Sabyasachi Mondal and published by Bentham Science Publishers. This book was released on 2024-05-20 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational simulation and experimental techniques for nanofluid flow is a collection of studies on nanofluid modelling. It brings together eight detailed research articles that describe the latest developments in nanofluid flow experimentation and simulation. Topics covered include numerical flow simulations and applications on MHD viscous nanofluid, bioconvective nanofluid, oblique nanofluid, Casson nanofluid, hybrid nanofluid, Darcy-Forchheimer hybrid nanofluid, magneto-radiative Ag-water nanofluid, and thixotropic nanofluid. Key Features - Includes eight chapters authored by experts in fluid mechanics and numerical simulation - Showcases significant and novel attempts on computational simulation modelling for developing new mathematical models on nanofluids at the research level - Highlights current research intended to advance mathematics and other areas of science and technology - Includes references for advanced readers This publication is essential for researchers and students, academicians who are learning nanofluid flow models. Readers involved in applied research and development projects involving nanofluids will also benefit from the information (environmentalists, technicians and biomedical engineers).

Download or read book Nanofluids written by Mohammad Mehdi Rashidi and published by Elsevier. This book was released on 2024-07-17 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nanofluids are a new class of heat transfer fluids engineered by dispersing and stably suspending nanoparticles in traditional heat transfer fluids. Recently they have obtained global attention from the scientific community owing to their unique properties and significant applications in different engineering fields. Nanofluids: Preparation, Applications and Simulation Methods provides a comprehensive review of recent advances in this important research field. Different approaches for preparing some remarkable families of nanofluids such as aluminum oxide-based nanofluids, CuO/Cu-based nanofluids, carbon nanotubes/graphene-based nanofluids, ZnO-based nanofluids, Fe3O4-based nanofluids, and SiO2-based nanofluids are discussed in detail as well as their current and potential applications. Different approaches for numerical, semi-analytical and analytical simulations are also discussed including molecular dynamics, the Lattice Boltzmann method, and spectral methods, as well as advanced analytical techniques such as the Differential Transform Method, the Homotopy Analysis Method, and Optimal Homotopy Analysis. The book will be a valuable reference resource for academic and industrial researchers, materials scientists and engineers, nanotechnologists, and chemists working in the development of nanomaterials and nanofluids for heat transfer in energy and engineering applications. - Covers the synthesis of nanostructures, preparation of nanofluids, different applications and proposed models for fluid mechanics and heat transfer - Presents recent advances on preparation methods, including green chemistry-based methods for preparation of nanomaterials and nanofluids - Includes novel model-based approaches such as molecular dynamics and Lattice Boltzmann methods - Delves into applications in renewable energy technologies and thermal management - Contains a Semi-analytical approach for solving Time-Fractional Navier-Stokes Equation

Download or read book Collocation and Galerkin Time Stepping Methods written by National Aeronautics and Space Adm Nasa and published by Independently Published. This book was released on 2019-01-13 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods. Huynh, H. T. Glenn Research Center NASA/TM-2011-216340, E-17277

Download or read book Frontiers in Physics Rising Stars written by Alex Hansen and published by Frontiers Media SA. This book was released on 2021-10-04 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Methods in Applied Sciences written by Luigi Rodino and published by MDPI. This book was released on 2020-03-13 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes the seven papers that contributed to the Special Issue of Mathematics entitled “Mathematical Methods in Applied Sciences”. The papers are authored by eminent specialists and aim at presenting to a broad audience some mathematical models which appear in different aspects of modern life. New results in Computational Mathematics are given as well. Emphasis is on Medicine and Public Health, in relation also with Social Sciences. The models in this collection apply in particular to the study of brain cells during a stroke, training management efficiency for elite athletes, and optimal surgical operation scheduling. Other models concern Industry and Economy, as well as Biology and Chemistry. Numerical Methods are represented in particular by scattered data interpolation, spectral collocation, and the use of eigenvalues and eigenvectors of the Laplacian matrix. This book will appeal to scientists, teachers, and graduate students in Mathematics, in particular Numerical Analysis, and will be of interest for scholars in Applied Sciences, particularly in Medicine and Public Health.

Download or read book 3 1 Formalism in General Relativity written by Éric Gourgoulhon and published by Springer. This book was released on 2012-02-27 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.

Download or read book Spectral hp Element Methods for Computational Fluid Dynamics written by George Karniadakis and published by American Chemical Society. This book was released on 2013-01-10 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revision of: Spectral/hp element methods for CFD. 1999.

Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 1052 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Methods for Electromagnetic Phenomena written by Wei Cai and published by Cambridge University Press. This book was released on 2013-01-03 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of its kind to cover a wide range of computational methods for electromagnetic phenomena, from atomistic to continuum scales, this integrated and balanced treatment of mathematical formulations, algorithms and the underlying physics enables us to engage in innovative and advanced interdisciplinary computational research.

Download or read book Special Functions and Analysis of Differential Equations written by Praveen Agarwal and published by CRC Press. This book was released on 2020-09-08 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.

Download or read book Spectral Methods in MATLAB written by Lloyd N. Trefethen and published by SIAM. This book was released on 2000-07-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Download or read book Spectral Methods for Time Dependent Problems written by Jan S. Hesthaven and published by Cambridge University Press. This book was released on 2007-01-11 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.