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Basic Concepts of Fluid Flow Read chapter Read first chapter

2020 | OriginalPaper | Chapter

7. Solution of the Navier–Stokes Equations: Part 1

Authors : Joel H. Ferziger, Milovan Perić, Robert L. Street

Published in: Computational Methods for Fluid Dynamics

Publisher: Springer International Publishing

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Abstract

The additional complexity of the Navier–Stokes equations and special features for incompressible flows are considered in this chapter and the next; here we cover basic issues, the features of the equations, and the methods of solution. The staggered and collocated variable arrangements, the pressure equation, and the pressure-velocity coupling for incompressible flows using the fractional-step and SIMPLE algorithms are described in detail. Other approaches (the PISO algorithm, streamfunction-vorticity, and artificial compressibility) are also briefly described. The initial and boundary conditions for the Navier–Stokes equations and their implementation on Cartesian grids are also covered.

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previous chapter Methods for Unsteady Problems
next chapter Solution of the Navier–Stokes Equations: Part 2
Footnotes
1
In flows where the density of the fluid varies with height in a gravitational field, the flow is said to be stratified, and the flow may carry heavy fluid up or light fluid down so that it now has a density different from its surroundings; the fluid then has not only kinetic energy, but also energy as a result of its position, called potential energy. The result is buoyant forces that are touched on later in this chapter and are very important in both meteorology and oceanography.
 
2
In this case the second-order extrapolation \(p^{n+1}=(3/2) p^{n+1/2}-(1/2) p^{n-1/2}\) is used.
 
3
Coupled (or monolithic) solvers are also available and most commercial packages now offer them; discussion of solver alternatives can be found in the code documentation or in the literature, e.g., Heil et al. (2008) or Malinen (2012). See also Chap. 11 for a brief description of one such method.
 
4
This relation was first derived by Raithby and Schneider (1979) and later re-discovered by Perić (1985) using different arguments.
 
Metadata
Title
Solution of the Navier–Stokes Equations: Part 1
Authors
Joel H. Ferziger
Milovan Perić
Robert L. Street
Copyright Year
2020
Book
Computational Methods for Fluid Dynamics

Print ISBN: 978-3-319-99691-2

Electronic ISBN: 978-3-319-99693-6

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-319-99693-6_7

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