Cell Velocity

Current velocities are computed normal to faces. However, in several computations, the cell average velocities are necessary. Here, the cell velocities are computed using the method of Perot (2000):

$\begin{array}{l}\displaystyle \textbf{V}_i = \frac{1}{A_i} \sum _{k \in \mathcal{K}(i) } \Delta x_{i,k} L_k (u_N)_k\end{array}$

where $\begin{array}{l}\Delta x_{i,k}\end{array}$ is the distance from the center of cell center i to edge center k, and $\begin{array}{l}L_k\end{array}$ is the length of face k. Because this method is explicit, all acceleration terms can be computed before the start of the outer iterations and do not need to be updated.