Spectral/hp Element Methods for Computational Fluid Dynamics / Edition 2

by George Em Karniadakis, Spencer J. Sherwin

Overview

Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretization procedures on unstructured meshes, which are also recognized as more efficient for solution of time-dependent oscillatory solutions over long time periods. Here Karniadakis and Sherwin present a much-updated and expanded version of their successful first edition covering the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing over 50% new material, including discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilization and filtering techniques, this text aims to introduce a wider audience to the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes. It provides a detailed explanation of the key concepts underlying the methods along with practical examples of their derivation and application, and is aimed at students, academics and practitioners in computational fluid mechanics, applied and numerical mathematics, computational mechanics, aerospace and mechanical engineering and climate/ocean modelling.

Product Details

ISBN-13:	9780198528692
Publisher:	Oxford University Press
Publication date:	08/11/2005
Series:	Numerical Mathematics and Scientific Computation
Edition description:	REV
Pages:	676
Product dimensions:	9.68(w) x 6.84(h) x 1.60(d)

About the Author

George Em Karniadakis is a Professor at Brown University, Division of Applied Mathematics, 182 George Street, Providence, RI 02912, USA. Spencer Sherwin is Reader in computational Fluid Mechanics, Department of Aeronautics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK.

Table of Contents

1. Introduction2. Fundamental Concepts in One Dimension3. Multi-dimensional Expansion Bases4. Multi-dimensional Formulations5. Diffusion Equation6. Advection and Advection-diffusion7. Non-conforming Elements8. Algorithms for Incompressible Flows9. Incompressible Flow Simulations: Verification and ValidationA Jacobi PolynomialsB Gauss-type IntegrationC Collocation DifferentiationD Co Discontinuous Expansion BasesE Characteristic Flux DecompositionReferencesIndex