The computational stability properties of the Shuman pressure gradient averaging technique
Schoenstadt, Arthur L.
Williams, R. T.
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The stability properties of the Shuman pressure gradient averaging technique are investigated with the linearized shallow water equations. In the simplest case an analytic expression is obtained for the stability region, and the maximum time step is shown to be twice the value for the leapfrog scheme. When a mean flow is added to the equations, it is shown the maximum time step must be reduced. The time averaging suggested by Robert is examined, and again leads to a shorter time step. In each case, however, the use of the Shuman averaging allows a significantly longer time step than the conventional leapfrog scheme