Supercritical Subcritical Mixed Flows

Flow can change with either time or distance along the routing reach from supercritical to subcritical while passing through critical flow, or conversely. This "mixed flow" requires special treatment to prevent numerical instabilities in the solution of the Saint-Venant equations. Such a treatment for mixed flows (Fread et al., 1996) is to provide a "local partial inertia" filter, i.e., which multiplies the first two (inertia) terms in the momentum equations [(30) and (51)]. Fr is the Froude number of the flow in any ith Ax reach, and the exponent (m) varies from 1 to 10, with 5 usually preferred, and 0.85 <Frc < 0.95 is the specified range for Frc. The filter takes on a value of zero when Fr > 1. The local partial inertia filter (a) avoids numerical difficulties associated with mixed flows while introducing negligible errors, less than about 1 to 2% for all flow conditions.

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