Second Upwind Differencing or Hybrid Scheme

According to the second upwind differencing, if u is the velocity in x direction and is any property which can be convected or diffused, then

(12.1)

One point to be carefully observed from Eq. (12.1) is that the second upwind should be written in conservative form.

Figure 12.1: Definition of u_R and u_L

Definition of

(12.2a)

Definition of

(12.2b)

Now,

for              for

(12.3)

and

for             for

(12.4)

Finally, for and we get

(12.5)