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nonlinear: 0,1, or 2

Advection scheme for momentum:

0
: No advection of momentum, i.e. $\mathbf{u}\cdot\nabla\mathbf{u}=0$.
1
: First-order upwind for momentum.
2
: Second-order central for momentum. Note that diffusion must be present for stability. While it is difficult to perform an exact stability analysis for the unstructured-grid equations, the 1-d stability limitation requires that grid Peclet number according to

\begin{displaymath}
Pe_\Delta<\frac{2}{C} ,
\end{displaymath}

where $Pe_\Delta = \frac{\max(\vert U\vert)\max(D_g)}{\min(\nu_H)}$ and $C=\frac{\max(\vert U\vert)\Delta t}{\max(D_g)}$, which translates into the requirement that the horizontal diffusion be restricted to

\begin{displaymath}
\nu_H>\frac{\max(\vert U\vert)^2\Delta t}{2} .
\end{displaymath}

Equivalently, the vertical diffusion is restricted by

\begin{displaymath}
\nu>\frac{\max(\vert w\vert)^2\Delta t}{2} .
\end{displaymath}



2014-08-06