Description
Book SynopsisSpectral 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 discretisation procedures on unstructured meshes, which are also recognised 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 stabilisation and filtering techniques, this text aims to introduce a wider audience to the use o
Trade ReviewThe book contains a large amount of material, including a number of exercises, examples and figures. The book will be helpful to specialists coming into contact with CFD, applied and numerical mathematicians, engineers, physicists and specialists in climate and ocean modeling. It can also be recommended for advanced students of these disciplines. * EMS Newsletter *
This book will probably help popularize the spectral/hp element method. Not only should it be recommended to researchers working on spectral/hp methods but it should also be on the wish list of all those who are interested in computational fluid dynamics. * Jean-Luc Guermond, Mathematical Reviews *
Table of ContentsIntroduction ; Fundamental concepts in one dimension ; Multi-dimensional expansion bases ; Multi-dimensional formulations ; Diffusion equation ; Advection and advection-diffusion ; Non-conforming elements ; Algorithms for incompressible flows ; Incompressible flow simulations:verification and validation ; Hyperbolic conservation laws ; Appendices ; Jacobi polynomials ; Gauss-Type integration ; Collocation differentiation ; Co discontinuous expansion bases ; Characteristic flux decomposition ; References ; Index
