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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. 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 ...

  4. 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 ...

  5. PISO algorithm - Wikipedia

    en.wikipedia.org/wiki/PISO_algorithm

    It is an extension of the SIMPLE algorithm used in computational fluid dynamics to solve the Navier-Stokes equations. PISO is a pressure-velocity calculation procedure for the Navier-Stokes equations developed originally for non-iterative computation of unsteady compressible flow, but it has been adapted successfully to steady-state problems.

  6. SIMPLEC algorithm - Wikipedia

    en.wikipedia.org/wiki/SIMPLEC_algorithm

    The steps involved are same as the SIMPLE algorithm and the algorithm is iterative in nature. p*, u*, v* are guessed Pressure, X-direction velocity and Y-direction velocity respectively, p', u', v' are the correction terms respectively and p, u, v are the correct fields respectively; Φ is the property for which we are solving and d terms are involved with the under relaxation factor.

  7. 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 ...

  8. 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 ...

  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 ...