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  2. Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/NavierStokes_equations

    The NavierStokes equations (/ n æ v ˈ j eɪ s t oʊ k s / nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades ...

  3. Derivation of the Navier–Stokes equations - Wikipedia

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

    The general form of the equations of motion is not "ready for use", the stress tensor is still unknown so that more information is needed; this information is normally some knowledge of the viscous behavior of the fluid. For different types of fluid flow this results in specific forms of the NavierStokes equations.

  4. Hydrodynamic stability - Wikipedia

    en.wikipedia.org/wiki/Hydrodynamic_stability

    The essential problem is modeled by nonlinear partial differential equations and the stability of known steady and unsteady solutions are examined. [1] The governing equations for almost all hydrodynamic stability problems are the NavierStokes equation and the continuity equation.

  5. SIMPLE algorithm - Wikipedia

    en.wikipedia.org/wiki/SIMPLE_algorithm

    In computational fluid dynamics (CFD), the SIMPLE algorithm is a widely used numerical procedure to solve the NavierStokes equations. SIMPLE is an acronym for Semi-Implicit Method for Pressure Linked Equations. The SIMPLE algorithm was developed by Prof. Brian Spalding and his student Suhas Patankar at Imperial College London in the early ...

  6. Turbulence modeling - Wikipedia

    en.wikipedia.org/wiki/Turbulence_modeling

    In computational fluid dynamics, the k–omega (k–ω) turbulence model [10] is a common two-equation turbulence model that is used as a closure for the Reynolds-averaged NavierStokes equations (RANS equations). The model attempts to predict turbulence by two partial differential equations for two variables, k and ω, with the first ...

  7. Rayleigh problem - Wikipedia

    en.wikipedia.org/wiki/Rayleigh_problem

    In fluid dynamics, Rayleigh problem also known as Stokes first problem is a problem of determining the flow created by a sudden movement of an infinitely long plate from rest, named after Lord Rayleigh and Sir George Stokes. This is considered as one of the simplest unsteady problems that have an exact solution for the Navier-Stokes equations.

  8. 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 ...

  9. Reynolds-averaged Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Reynolds-averaged_Navier...

    The Reynolds-averaged NavierStokes equations (RANS equations) are time-averaged [a] equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition , whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds . [ 1 ]

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