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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).

Applications and related fields

For general continuum mechanics, See 73BXX, or other parts of 73-XX

This image slightly hand-edited for clarity.

Subfields

• 76A: Foundations, constitutive equations, rheology
• 76B: Incompressible inviscid fluids, potential theory
• 76C: Incompressible inviscid fluids, vorticity flows
• 76D: Incompressible viscous fluids
• 76E: Hydrodynamic stability
• 76G25: General aerodynamics and subsonic flows
• 76H05: Transonic flows
• 76J20: Supersonic flows
• 76K05: Hypersonic flows
• 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
• 76W05: Magnetohydrodynamics and electrohydrodynamics
• 76X05: Ionized gas flow in electromagnetic fields; plasmic flow

(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

CFD codes

nekton - fluid flow and heat transfer