Consistency with continuity in conservative advection schemes for free‐surface models

The consistency of the discretization of the scalar advection equation with the discretization of the continuity equation is studied for conservative advection schemes coupled to three-dimensional flows with a free-surface. Consistency between the discretized free-surface equation and the discretized scalar transport equation is shown to be necessary for preservation of constants. In addition, this property is shown to hold for a general formulation of conservative schemes. A discrete maximum principle is proven for consistent upwind schemes. Various numerical examples in idealized and realistic test cases demonstrate the practical importance of the consistency with the discretization of the continuity equation. Copyright © 2002 John Wiley & Sons, Ltd.

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