5.2 – UDS (Upstream Differencing Scheme)

In order to avoid possible negative coefficients and numerical oscillations, which are discussed in [1], we shall use UDS. Hence, the interpolation functions have the following expressions:



;


;


(5.2.4a)


;
;

(5.2.4b)

;
;

(5.2.4c)

;
;


(5.2.4d)

Comparing (5.2.4) to (4.6), we have:



se


se




(5.2.5a)

se
se		  

And also,
         
   
   
(5.2.5b)

Subscript i symbolize the faces, which are being interpolated.

Notice that the diffusive terms are approximated by central differences.

Notice: The UDS generates solutions that are physically coherent, although it has the property of softening high gradients. This occurs because this is a dissipative scheme.

 
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