Abstract
Abstract Steady free-surface flows under the influence of gravity are considered in this paper. The appropriate variational principle is derived, where the stream function within the flow and the free-surface elevation are independently subjected to variation. The formulation of the principle in terms of linear finite elements is presented, and the resulting set of non-linear equations is reduced to the iterative solution of a linear set. The computations are shown to be convergent regardless of whether the Froude number of the stream is greater or less than unity, and independent tests show that the accuracy of the results is well within the usual range expected for internal flows when linear elements are used.
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