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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.
Using these properties, the Navier–Stokes equations of motion, expressed in tensor notation, are (for an incompressible Newtonian fluid): = + = + where is a vector representing external forces. Next, each instantaneous quantity can be split into time-averaged and fluctuating components, and the resulting equation time-averaged, [ b ] to yield:
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.
Compressible Navier-Stokes equations (C-NS): Start with the CCL. Assume a Newtonian viscous stress tensor (see Newtonian fluid) and a Fourier heat flux (see heat flux). [44] [45] The C-NS need to be augmented with an EOS and a caloric EOS to have a closed system of equations. Incompressible Navier-Stokes equations (I-NS): Start with the C-NS.
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.
So the incompressible Navier-Stokes equation can be simply written: = + + In fact, note that for the incompressible flow the strain rate is purely deviatoric since there is no dilation (e=0). In other words, for an incompressible flow the isotropic stress component is simply the pressure:
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 ...