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Applied Shape Optimization for Fluids$
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Bijan Mohammadi and Olivier Pironneau

Print publication date: 2009

Print ISBN-13: 9780199546909

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199546909.001.0001

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Partial differential equations for fluids

Partial differential equations for fluids

Chapter:
(p.41) 3 Partial differential equations for fluids
Source:
Applied Shape Optimization for Fluids
Author(s):

Bijan Mohammadi

Olivier Pironneau

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199546909.003.0003

This chapter describes the governing equations considered throughout the book. The equations of fluid dynamics are recalled, together with the k-epsilon turbulence model, which is used later on for high Reynolds number flows when the topology of the answer is not known. The fundamental equations of fluid dynamics are recalled; this is because applied OSD for fluids requires a good understanding of the state equation: Euler and Navier–Stokes equations in this case, with and without turbulence models together with the inviscid and/or incompressible limits. The chapter recalls wall-laws also used for OSD as low complexity models. By wall-laws domain decomposition with a reduced dimension model near the wall is understood. In other words, there is no universal wall-laws and when using a wall-function, it needs to be compatible with the model used far from the wall. Large eddy simulation is giving a new life to the wall-functions especially to simulate high-Reynolds external flows.

Keywords:   Euler equation, Navier–Stokes equations, incompressible limits, low complexity models, wall-function, turbulence modelling

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