Chapter

Partial differential equations for fluids

Bijan Mohammadi and Olivier Pironneau

in Applied Shape Optimization for Fluids

Second edition

Published in print September 2009 | ISBN: 9780199546909
Published online February 2010 | e-ISBN: 9780191720482 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199546909.003.0003

Series: Numerical Mathematics and Scientific Computation

 Partial differential equations for fluids

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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

Chapter.  5031 words. 

Subjects: Mathematical and Statistical Physics

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