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Pressure-correction method is a class of methods used in computational fluid dynamics for numerically solving the Navier-Stokes equations normally for incompressible flows. Common properties [ edit ]
The incompressible Navier–Stokes equation is a differential algebraic equation, having the inconvenient feature that there is no explicit mechanism for advancing the pressure in time. Consequently, much effort has been expended to eliminate the pressure from all or part of the computational process.
In computational fluid dynamics, the projection method, also called Chorin's projection method, is an effective means of numerically solving time-dependent incompressible fluid-flow problems. It was originally introduced by Alexandre Chorin in 1967 [1] [2] as an efficient means of solving the incompressible Navier-Stokes equations.
In fluid mechanics, non-dimensionalization of the Navier–Stokes equations is the conversion of the Navier–Stokes 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 ...
In the analysis of a flow, it is often desirable to reduce the number of equations and/or the number of variables. The incompressible Navier–Stokes equation with mass continuity (four equations in four unknowns) can be reduced to a single equation with a single dependent variable in 2D, or one vector equation in 3D.
The small time behavior of the flow is then found through simplification of the incompressible Navier–Stokes equations using the initial flow to give a step-by-step solution as time progresses. An exact solution in two spatial dimensions is known, and is presented below. Animation of a Taylor-Green Vortex using colour coded Lagrangian tracers
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 Navier–Stokes equations (RANS). This is done by means of "a priori" tests, in which the input data for the model ...
Discretization of the Navier–Stokes equations of fluid dynamics is a reformulation of the equations in such a way that they can be applied to computational fluid dynamics. Several methods of discretization can be applied: Finite volume method; Finite elements method; Finite difference method