Chapter

Continuous media and viscous fluids

D. Violeau

in Fluid Mechanics and the SPH Method

Published in print May 2012 | ISBN: 9780199655526
Published online September 2012 | e-ISBN: 9780191741227 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199655526.003.0003
Continuous media and viscous fluids

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Continuous media are here seen from the traditional viewpoint of balance equations; the chapter introduces the concepts of mesoscopic particles, fields and fluxes. The conservation laws of the first two chapters are revisited in this framework. The Cauchy stress tensor is then considered and estimated from thermodynamical considerations for a viscous fluid, with emphasis on incompressible (or weakly compressible) flows, leading to the Navier–Stokes and Euler equations of motion. also talks about similarity, about the particular role of pressure for incompressible flows and describe surface tension. Lastly, the Navier–Stokes equations are revisited from the Boltzmann equation introduced in Chapter 2, and the author gives a personal viewpoint of variational principles for continuous fluid mechanics.

Keywords: Continuous media; balance equations; viscous fluids; Navier–Stokes equations; similarity

Chapter.  40632 words.  Illustrated.

Subjects: Condensed Matter Physics

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