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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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ALGORITHMS FOR INCOMPRESSIBLE FLOWS

ALGORITHMS FOR INCOMPRESSIBLE FLOWS

Chapter:
(p.400) 8 ALGORITHMS FOR INCOMPRESSIBLE FLOWS
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/9780198528692.003.0008

This chapter presents different ways of formulating the incompressible Navier-Stokes equations based on primitive variables, that is, velocity and pressure, as well as velocity-vorticity algorithms. It considers both coupled, splitting, and least-squares formulations for primitive variables. Both the Uzawa coupled algorithm and a new substructured solver are discussed. The discussion on primitive variables time-splitting includes recent theoretical advances in the pressure-correction and velocity correction schemes as well as the rotational formulation of the pressure boundary condition. The final section is devoted to nonlinear terms; it includes a discussion of spatial and temporal discretization with focus on the semi-Lagrangian method for the incompressible Navier-Stokes equations.

Keywords:   Navier-Stokes equations, velocity, pressure, velocity-vorticity algorithms, Uzawa algorithm, substructured Stokes system, primitive variables, nonlinear terms

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