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Author Deville, M. O. (Michel O.), author
Title High-order methods for incompressible fluid flow / M.O. Deville, P.F. Fischer, E.H. Mund
Imprint Cambridge : Cambridge University Press, 2002
book jacket
Descript 1 online resource (xxvii, 499 pages) : digital, PDF file(s)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Cambridge monographs on applied and computational mathematics ; 9
Cambridge monographs on applied and computational mathematics ; 9
Note Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Fluid Mechanics and Computation: An Introduction -- Viscous Fluid Flows -- Mass Conservation -- Momentum Equations -- Linear Momentum -- Angular Momentum -- Energy Conservation -- Thermodynamics and Constitutive Equations -- Fluid Flow Equations and Boundary Conditions -- Isothermal Incompressible Flow -- Thermal Convection: The Boussinesq Approximation -- Boundary and Initial Conditions -- Dimensional Analysis and Reduced Equations -- Vorticity Equation -- Simplified Models -- Turbulence and Challenges -- Numerical Simulation -- Hardware Issues -- Software Issues -- Algorithms -- Advantages of High-Order Methods -- Approximation Methods for Elliptic Problems -- Variational Form of Boundary-Value Problems -- Variational Functionals -- Boundary Conditions -- Sobolev Spaces and the Lax-Milgram Theorem -- An Approximation Framework -- Galerkin Approximations -- Collocation Approximation -- Finite-Element Methods -- The h-Version of Finite Elements -- The p-Version of Finite Elements -- Spectral-Element Methods -- Orthogonal Collocation -- Orthogonal Collocation in a Monodomain -- Orthogonal Collocation in a Multidomain -- Error Estimation -- Solution Techniques -- The Conditioning of a Matrix -- Basic Iterative Methods -- Preconditioning Schemes of High-Order Methods -- Iterative Methods Based on Projection -- A Numerical Example -- Parabolic and Hyperbolic Problems -- Time Discretization Schemes -- Linear Multistep Methods -- Predictor-Corrector Methods -- Runge-Kutta Methods -- Splitting Methods
High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular attention given to enforcement of incompressibility. Advanced discretizations, implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications. Computer scientists, engineers and applied mathematicians interested in developing software for solving flow problems will find this book a valuable reference
TAEBDC; 2009
Link Print version: 9780521453097
Subject Fluid dynamics
Alt Author Fischer, P. F. (Paul F.), author
Mund, E. H. (Ernest H.), author
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