5.3 – WUDS (Weighted Upstream Differencing Scheme)

5.3 – WUDS (Weighted Upstream Differencing Scheme)
In this scheme, the coefficients and are used as weight between convection and diffusion, they are dependents of Peclet Number (Pe), this gives us relations between convective and diffusive flows. The Peclet number is eventually defined as follows:
			(5.3.1)
And,
	= Peclet of grid, evaluated for the elemental volume;
Therefore,
		« Reynolds of grid	(5.3.2)
And also,

With,
		« Used in energy equation	(5.3.3a)
And this may be interpreted as,
		« Used in momentum equation	(5.3.3b)
From this analysis concerning to the Peclet number, it is possible to conclude that:
			(5.3.4)
Notice that this equation is the classical definition of Pe as a relation between the convective and diffusive fluxes. The expressions for and , in equations 5.3.5, are based on the exponential scheme that uses interpolation functions obtained from the exact solution of the one-dimensional convection / diffusion problem.
			(5.3.5a)
And,
			(5.3.5b)
Subscript i represent the face that is being interpolated.


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