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  2. Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/NavierStokes_equations

    Expressing the NavierStokes vector equation in Cartesian coordinates is quite straightforward and not much influenced by the number of dimensions of the euclidean space employed, and this is the case also for the first-order terms (like the variation and convection ones) also in non-cartesian orthogonal coordinate systems.

  3. Non-dimensionalization and scaling of the Navier–Stokes ...

    en.wikipedia.org/wiki/Non-dimensionalization_and...

    In fluid mechanics, non-dimensionalization of the NavierStokes equations is the conversion of the NavierStokes equation to a nondimensional form. This technique can ease the analysis of the problem at hand, and reduce the number of free parameters. Small or large sizes of certain dimensionless parameters indicate the importance of certain ...

  4. Direct numerical simulation - Wikipedia

    en.wikipedia.org/wiki/Direct_numerical_simulation

    Also, direct numerical simulations are useful in the development of turbulence models for practical applications, such as sub-grid scale models for large eddy simulation (LES) and models for methods that solve the Reynolds-averaged NavierStokes equations (RANS). This is done by means of "a priori" tests, in which the input data for the model ...

  5. Burgers vortex - Wikipedia

    en.wikipedia.org/wiki/Burgers_vortex

    Burgers vortex layer or Burgers vortex sheet is a strained shear layer, which is a two-dimensional analogue of Burgers vortex. This is also an exact solution of the NavierStokes equations, first described by Albert A. Townsend in 1951. [8] The velocity field (,,) expressed in the Cartesian coordinates are

  6. Derivation of the Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Derivation_of_the_Navier...

    The NavierStokes equations are based on the assumption that the fluid, at the scale of interest, is a continuum – a continuous substance rather than discrete particles. Another necessary assumption is that all the fields of interest including pressure , flow velocity , density , and temperature are at least weakly differentiable .

  7. Continuity equation - Wikipedia

    en.wikipedia.org/wiki/Continuity_equation

    The NavierStokes equations form a vector continuity equation describing the conservation of linear momentum. If the fluid is incompressible (volumetric strain rate is zero), the mass continuity equation simplifies to a volume continuity equation: [ 3 ] ∇ ⋅ u = 0 , {\displaystyle \nabla \cdot \mathbf {u} =0,} which means that the ...

  8. Reynolds stress - Wikipedia

    en.wikipedia.org/wiki/Reynolds_Stress

    One splits the Euler equations (fluid dynamics) or the Navier-Stokes equations into an average and a fluctuating part. One finds that upon averaging the fluid equations, a stress on the right hand side appears of the form ρ u i ′ u j ′ ¯ {\displaystyle \rho {\overline {u'_{i}u'_{j}}}} .

  9. Navier–Stokes existence and smoothness - Wikipedia

    en.wikipedia.org/wiki/NavierStokes_existence...

    In mathematics, the NavierStokes equations are a system of nonlinear partial differential equations for abstract vector fields of any size. In physics and engineering, they are a system of equations that model the motion of liquids or non-rarefied gases (in which the mean free path is short enough so that it can be thought of as a continuum mean instead of a collection of particles) using ...