2.4.5 Donor cell (FTBS) scheme

Figure 11: Stencil and example for donor cell scheme: result is wonderfully smooth but smeared out almost beyond recognition.

Figure 11 shows the stencil diagram and an example for the donor cell scheme (FTBS, 1st order upwind method), with flux at $i+\frac{1}{2}$

$$\textstyle f_{i+\frac{1}{2}}^n = f \! \left( \rho_{i}^n \right) \enspace .$$ (108)