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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 76: Fluid mechanics

Introduction

Fluid mechanics studies air, water, and other fluids in motion: compression, turbulence, diffusion, wave propagation, and so on. Mathematically this includes study of solutions of differential equations, including large-scale numerical methods (e.g the finite-element method), although the development of those techniques is more properly in section 65 (Numerical Analysis).

History

Applications and related fields

For general continuum mechanics, See 74AXX, or other parts of 74-XX

This image slightly hand-edited for clarity.

Subfields

• 76A: Foundations, constitutive equations, rheology
• 76B: Incompressible inviscid fluids, potential theory
• 76D: Incompressible viscous fluids
• 76E: Hydrodynamic stability
• 76F: Turbulence, see also 58F13, 58F27, 60GXX, 60JXX
• 76G25: General aerodynamics and subsonic flows
• 76H05: Transonic flows
• 76J20: Supersonic flows
• 76K05: Hypersonic flows
• 76L05: Shock waves and blast waves, See also 35L67
• 76M: Basic methods in fluid mechanics, see also 65-XX
• 76N: Compressible fluids and gas dynamics, general
• 76P05: Rarefied gas flows, Boltzmann equation, See also 82B40, 82C40, 82D05
• 76Q05: Hydro- and aero-acoustics
• 76R: Diffusion and convection
• 76S05: Flows in porous media; filtration; Seepage
• 76T: Two-phase and multiphase flows
• 76U05: Rotating fluids
• 76V05: Reaction effects in flows [See also 80A32]
• 76W05: Magnetohydrodynamics and electrohydrodynamics
• 76X05: Ionized gas flow in electromagnetic fields; plasmic flow
• 76Y05: Quantum hydrodynamics and relativistic hydrodynamics, See also 83C55, 85A30
• 76Z: Biological fluid mechanics, see also 92CXX

(Fluid Dynamics is divided into more subareas than any other discipline, in the MSC scheme!)

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

Belotserkovskii, O. M.: "CFD state-of-the-art in the U.S.S.R.", The Second World Congress of Computational Mechanics, Part II (Stuttgart, 1990). Internat. J. Numer. Methods Engrg. 34 (1992), no. 2, 395--415. MR93a:76063

Comte, Pierre: "(A primer to) numerical methods for compressible flows", Mécanique des fluides numérique (Les Houches, 1993), 165--219; North-Holland, Amsterdam, 1996. CMP1426154

Tanner, Roger I.: "Constitutive equations for the computing person", Viscoelasticity and rheology (Madison, Wis., 1984), 421--439; Academic Press, Orlando, Fla., 1985. MR87j:76020

Newsgroup sci.mech.fluids, sci.physics.computational.fluid-dynamics

There is a considerable collection of useful formulas for wind calculations and so on at the Aviation Formulary.

Software and tables

nekton - fluid flow and heat transfer

Other web sites with this focus

• CPED Heat Transfer and Fluid Flow Group
• CFD Online - many links
• CFD WWW home pages list
• Here are the AMS and Goettingen resource pages for area 76.
• The Net Advance of Physics
• UTK archives page

Selected Topics at this site

• The diffusion equation (dC/dt = d^2 C / dx^2)
• Boundary layers in slightly viscous flow (numerical Navier-Stokes equations)
• Terminal velocity of a coin falling through air (stable approximations)
• Fluid mechanics and dimensional analysis applied to model planes!
• Aerodynamic study of the flights of insects. (They said it couldn't be done...)
• Pointers to the history of computational fluid dynamics.