Abstract
The solution of the Navier-Stokes equations in velocity-pressure variables is the subject of this chapter. This set of equations is of broader application than the vorticity-streamfunction equations which are restricted to two-dimensional flows. First, the Fourier method for computing fully periodic flows is discussed. Then the major part of the chapter is devoted to the case of one or more nonperiodic directions. In such a situation, the classical difficulty is the determination of the pressure field ensuring that the velocity field is solenoidal. This problem is discussed according to the kind of method used for the advancement in time. Time-discretization methods leading, at each time-cycle, either to a Stokes problem or to a combination of Helmholtz and Darcy problems will be considered. Various solution methods will be discussed and compared in typical examples. Finally, an application to the calculation of a three-dimensional rotating flow will be presented.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Peyret, R. (2002). Velocity-Pressure Equations. In: Spectral Methods for Incompressible Viscous Flow. Applied Mathematical Sciences, vol 148. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-6557-1_8
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6557-1_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2913-6
Online ISBN: 978-1-4757-6557-1
eBook Packages: Springer Book Archive