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Compressible flow
24 related topics
Incompressible flow
29 related topics
Properties
24 related topics
Exact solutions of the Navier–Stokes equations
19 related topics
Key facts & relationships
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Overview
- Viscous Viscosity
- Partial differential equations Partial differential equation
- Claude-Louis Navier
- George Gabriel Stokes Sir George Stokes, 1st Baronet
- Siméon Denis Poisson
- Momentum
- Newtonian fluid
- Mass conservation Conservation of mass
- Equation of state
- Pressure
- Temperature
- Density
- Newton's second law
- Fluid motion Fluid dynamics
- Stress Stress (mechanics)
- Gradient
- Euler equations Euler equations (fluid dynamics)
- Inviscid flow
- Aircraft Aircraft design process
- Blood flow Hemodynamics
- Power stations Power station
- Pollution
- Maxwell's equations
- Magnetohydrodynamics
- Smooth Smoothness
- Navier–Stokes existence and smoothness
- Clay Mathematics Institute
- Seven most important open problems in mathematics Millennium Prize Problems
- Dirichlet Dirichlet boundary condition
- Neumann boundary condition
Flow velocity
- Flow velocity
- Vector field
- Fluid
- Dynamical equations Dynamical systems
- Classical mechanics
- Trajectories
- Particle
- Continuum Continuum (theory)
- Streamlines Streamlines, streaklines, and pathlines
- Integral curves Integral curve
General continuum equations
- Cauchy momentum equation
- Cauchy stress tensor
- Deviatoric stress tensor Deviatoric stress
- Material derivative
- Divergence
- Time
- Body accelerations Body force
- Gravity
- Inertial accelerations Fictitious force
- Electrostatic accelerations Coulomb's law
- Homogenous
- Mass
- Integration throughout the volume Volume integral
- Partial derivative
- Scalar field
- Outer product
- Constitutive relation
- Velocity Shear velocity
Compressible flow
- Incompressible flow section Navier–Stokes equations
- Galilean invariant Galilean invariance
- Elasticity tensor
- Double-dot product Dyadics
- Isotropic
- Helmholtz decomposition
- Lamé parameters
- Second viscosity
- Dynamic viscosity
- Linear elasticity
- Constitutive equation
- Trace Trace (linear algebra)
- Second viscosity Volume viscosity
- Thermal hydraulics
- Isotropic stress Hydrostatic stress
- Deviatoric stress tensor
- Transport coefficient
- Conservation variables Conservation variable?action=edit&redlink=1
- Kinematic viscosity
- Lamb vector
- Incompressible flow
- Fluid elements Fluid element
- Isochoric flow Isochoric process
- Solenoidal Solenoidal vector field
Incompressible flow
- Strain tensor
- Conservative variables Conservative variable?action=edit&redlink=1
- Shock waves Shock wave
- Mach numbers Mach number
- Pressure head
- Poisson equation
- Shear stress
- Vector Laplacian
- Heat conduction
- Diffusion equation
- Stokes equations Stokes flow
- Convection–diffusion equations Convection–diffusion equation
- Conservative field
- Hydraulic head
- Hydraulics
- Euclidean space
- Orthogonal coordinate
- Cartesian Cartesian coordinate system
- Cylindrical Cylindrical coordinate system
- Spherical Spherical coordinate system
- Tensor calculus
- Bernoulli's equation
- Irrotational Conservative vector field
- Integro-differential equation
- Biot–Savart's law Biot–Savart law
- Basis functions Basis function
- Line integral
- Stokes' theorem
- Plate-bending Bending of plates
Non-inertial frame of reference
Other equations
- No-slip No-slip condition
- Capillary surface
- Balance of energy First law of thermodynamics (fluid mechanics)
- Divergence-free vector field Divergence-free
- Vector Laplace operator
- Vorticity
Stream function for incompressible 2D fluid
- Curl Curl (mathematics)
- Conservative force
- Stream function
- Biharmonic operator
- Jacobian determinant Jacobian matrix and determinant
- Creeping flow
- Axisymmetric
- Stokes stream function
- Scalar Scalar (mathematics)
- Differential algebraic equation
Properties
- Nonlinear Nonlinearity
- Partial differential equations
- Turbulence
- Convective
- Laminar Laminar flow
- Nozzle
- Chaotic Chaos theory
- Inertia
- Reynolds number
- Direct numerical simulation
- Reynolds-averaged Navier–Stokes equations
- Computational fluid dynamics
- Spalart–Allmaras Spalart–Allmaras turbulence model
- K–ω K-omega turbulence model
- K–ε Turbulence kinetic energy
- SST SST (Menter's Shear Stress Transport)?action=edit&redlink=1
- Large eddy simulation
- Continuum Continuum mechanics
- Relativistic velocities Relativistic velocity
- Capillarity
- Knudsen number
- Boltzmann equation
- Molecular dynamics
- Linear
Application to specific problems
- Multiphase flow
- Surface tension
- Scale analysis Scale analysis (mathematics)
- Boundary value problem
- Ordinary differential equation
- Implicit Implicit function
- Elliptic integrals Elliptic integral
- Roots of cubic polynomials Cubic formula
- √2 Square root of 2
- Rayleigh–Bénard convection
Exact solutions of the Navier–Stokes equations
- Poiseuille flow Hagen-Poiseuille equation
- Couette flow
- Stokes boundary layer
- Jeffery–Hamel flow
- Von Kármán swirling flow
- Stagnation point flow
- Landau–Squire jet
- Taylor–Green vortex
- Self-similar Self-similar solution
- Kummer's functions Kummer's function
- Whittaker functions Whittaker function
- Polytropic Polytrope
- Polar coordinates
- Cartesian coordinates
- Hopf fibration
- Pythagorean quadruple
- Torus
- Helicity Hydrodynamical helicity
- Beltrami flow
Wyld diagrams
- Graphs Graph (discrete mathematics)
- Perturbation expansion Perturbation theory
- Feynman diagrams Feynman diagram
- Quantum field theory
- Mstislav Keldysh
- Graphs Graph theory
- Correlated Correlation function
- Stochastic processes
- Pseudo-random
- Functions Function (mathematics)
- Probability distributions Probability distribution
Representations in 3D
General references
- Oxford University Press
- ISBN ISBN (identifier)
- Batchelor, G. K. George Batchelor
- McGraw-Hill
- V. Girault Vivette Girault
- Landau, L. D. Lev Landau
- Lifshitz, E. M. Evgeny Lifshitz
- Course of Theoretical Physics
- OCLC OCLC (identifier)
- Presses polytechniques et universitaires romandes
- Milne-Thomson, L.M. L. M. Milne-Thomson
- C.B.E Order of the British Empire
- Birkhoff, Garrett Garrett Birkhoff
- Döring, C.E. Charles R. Doering
- Basset, A.B. Alfred Barnard Basset
- Lions, P-L Pierre-Louis Lions
- Lamb, H. Horace Lamb
- White, Frank M. Frank M. White
Advanced semantic analysis
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Navier–Stokes equations
Nodes236
Edges235
Triples205
Avg. degree1.99
Density0.008475
Components1
How this topic connects Entity context
Quick relationship hints grouped by predicate. Useful for spotting recurring semantic connections around the current entity.See the strongest relationship patterns around the current topic before diving into the raw triples.
Navier–Stokes equations
Top relations
related to General references · 104
Navier–Stokes equations → Acheson, ACM Chelsea Publishing, Alexander, Algorithms, An Introduction, Applied, Applied Analysis, Basset, Batchelor, Bell, Cambridge, Cambridge University Press, Checkisbnvalue, Chemical Engineering, Clarendon Press, Co Ltd, CoFox, Complex Fluids, Computational Mathematics, Computing Science Series
related to Exact solutions of the Navier–Stokes equations · 22
Navier–Stokes equations → But, Cartesian, Couette, Examples, For, Green, Hamel, Jeffery, Kummer's, Landau, Navier, Note, Poiseuille, Reynolds, Some, Squire, Stokes, Taylor, Time-dependent, Under
related to Turbulence · 18
Navier–Stokes equations → Allmaras, Attempts, CFD, It, Large, LES, Navier, RANS, Reynolds, Reynolds-averaged Navier, Some, Spalart, SST, Stokes, The, This, To, Turbulence
related to A three-dimensional steady-state vortex solution · 11
Navier–Stokes equations → Clay Millennium, Hopf, It, Let, Navier, Note, One, Other, Pythagorean, Stokes, This
related to Applicability · 9
Navier–Stokes equations → At, Boltzmann, Failing, For, Knudsen, Navier, Stokes, The Navier, Together
related to Radial flow · 8
Navier–Stokes equations → Difficulties, Issues, Navier, Reynolds, Rf, Stokes, The, This
related to Nonlinearity · 7
Navier–Stokes equations → An, Hence, In, Stokes, Such, The, The Navier
related to Wyld diagrams · 7
Navier–Stokes equations → Feynman, In, Mstislav Keldysh's, Navier, Similar, Stokes, Wyld
related to External links · 5
Navier–Stokes equations → Glenn Research Center, NASA, Navier, Simplified, Stokes
related to Application to specific problems · 4
Navier–Stokes equations → Generally, Stokes, The Navier, This
Important terminology Word statistics
Frequent words and multi-word phrases across the lead, headings, infobox and body. Useful for terminology coverage.Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
Important terminology
equations displaystyle stokes navier equation flow fluid velocity mathbf left textstyle right pressure frac nabla partial incompressible cdot rho mu
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Navier–Stokes equations | is a | second most commonly seen | 0.90 | text |
| sound absorption | instance of | that is whenever we are not dealing with processes | 0.80 | text |
| attenuation of shock waves | instance of | that is whenever we are not dealing with processes | 0.80 | text |
| where second viscosity coefficient becomes important | instance of | that is whenever we are not dealing with processes | 0.80 | text |
| the Reynolds-averaged Navier | instance of | time-averaged equations | 0.80 | text |
| atoms or molecules | instance of | it is infinitely divisible and not composed of particles | 0.80 | text |
| Navier–Stokes equations | related to A three-dimensional steady-state vortex solution | Hopf | 0.60 | section |
| Navier–Stokes equations | related to A three-dimensional steady-state vortex solution | Let | 0.60 | section |
| Navier–Stokes equations | related to A three-dimensional steady-state vortex solution | One | 0.60 | section |
| Navier–Stokes equations | related to A three-dimensional steady-state vortex solution | This | 0.60 | section |
| Navier–Stokes equations | related to A three-dimensional steady-state vortex solution | Note | 0.60 | section |
| Navier–Stokes equations | related to A three-dimensional steady-state vortex solution | Clay Millennium | 0.60 | section |
No triples extracted yet.
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