3.2.1 Velocity at cell boundary

• With velocity possibly varying from cell to cell one needs to define an appropriate value at the cell boundary.

A logical choice is the shock speed from Eq. (169) which results in

$$v_{i+\frac{1}{2}} = \left\{ \begin{array}{ll} \frac{f \... ... & \mbox{if} \enspace q_{i+1}^n = q_i^n \end{array} \right.$$ (180)

or for Burgers' equation from Eq. (170) simply

$$v_{i+\frac{1}{2}} = \frac{1}{2} \left( v_{i}^n + v_{i+1}^n \right) \enspace .$$ (181)