First-Order Upwind

For a first-order upwind scheme, the convective flux is computed as:

(341)

This scheme introduces a dissipative error that is stabilizing and helps the solver achieve robust convergence. However, the numerical dissipation thus introduced has the effect of "smearing" discontinuities, particularly if those discontinuities are not aligned with the grid lines. Generally, this option would only be selected if a solution using the second-order convection was unobtainable. It is also fairly common practice to obtain an initial solution using the first-order convection and then switch to the second-order one to obtain a more accurate, final converged solution.