Jump to ContentJump to Main Navigation
Spectral/hp Element Methods for Computational Fluid Dynamics$
Users without a subscription are not able to see the full content.

George Karniadakis and Spencer Sherwin

Print publication date: 2005

Print ISBN-13: 9780198528692

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198528692.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 29 October 2020



Spectral/hp Element Methods for Computational Fluid Dynamics

George Em Karniadakis (Contributor Webpage)

Spencer J. Sherwin

Oxford University Press

This chapter completes the multi-dimensional formulation by explaining how the two- and three-dimensional expansions developed in Chapter 3 can be extended into a tessellation of multiple domains. These extensions are decomposed into three sections: local operations such as integration and differentiation; global operations such as the construction of global matrix systems; and pre- and post-processing issues such as boundary representation, high-order mesh generation, and particle tracking. A matrix formulation is introduced to help illustrate the algebraic systems that need to be constructed when computationally implementing the spectral/hp method. Formulation of both Galerkin and collocation projections are considered in this manner. The exercises at the end of the chapter include implementation of a two-dimensional spectral/hp element solver for a multi-element Galerkin projection.

Keywords:   integration, differentiation, surface Jacobian, global operations, Galerkin projection, spectral/hp element discretizations

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .