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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 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
• 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