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 (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 22 October 2019

ADVECTION AND ADVECTION DIFFUSION

ADVECTION AND ADVECTION DIFFUSION

Chapter:
(p.298) 6 ADVECTION AND ADVECTION DIFFUSION
Source:
Spectral/hp Element Methods for Computational Fluid Dynamics
Author(s):

George Em Karniadakis (Contributor Webpage)

Spencer J. Sherwin

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198528692.003.0006

This chapter focuses on the scalar advection equation and develops a Galerkin discretization using the techniques described in Chapter 4. It includes an extended presentation of the discontinuous Galerkin formulation for advection equations. Eigenspectra of the advection operators in both two and three dimensions are reviewed, which are relevant for explicit time stepping. Two forms of a semi-Lagrangian method for advection (strong and auxiliary forms) that could potentially prove very effective in enhancing the speed and accuracy of spectral/hp element methods in advection-dominated problems are discussed. A new section on stabilization techniques is introduced that discusses filters, spectral vanishing viscosity, and upwind collocation.

Keywords:   linear advection equation, Galerkin discretization, eigenspectra, advection operator, semi-Lagrangian formulation

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 .