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Spectral/hp Element Methods for Computational Fluid Dynamics$
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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

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HYPERBOLIC CONSERVATION LAWS

HYPERBOLIC CONSERVATION LAWS

Chapter:
(p.514) 10 HYPERBOLIC CONSERVATION LAWS
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/9780198528692.003.0010

This chapter discusses compressible Euler and Navier-Stokes equations as well as general hyperbolic conservation laws. The principle issue is how effectively to use the high-order expansions of the spectral/hp method whilst honouring the inherent monotonicity and conservation properties of the analytic system. Different ways of dealing with these fundamental issues for both the Euler and the Navier-Stokes equations are considered. A new section for the shallow water equations is also included and the section on the discontinuous Galerkin method has been rewritten. Finally, the last section discusses modeling of plasma flows, i.e., the so-called magneto-hydrodynamic (MHD) equations.

Keywords:   Euler equations, Navier-Stokes equations, shallow-water equations, shock-fitting techniques, magneto-hydrodynamics, monotonicity

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