Computation of Supercritical Free‐Surface Flows

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Abstract
Computational methods for the solution of two‐dimensional shallow‐water equations in steady, supercritical flow are presented. The limitations of these equations and criteria regarding their applicability to the solution of supercritical flows are discussed. Two explicit, shockcapturing, finite‐difference schemes—Lax and MacCormack—are investigated. The boundary conditions along walls require careful attention for a successful implementation of these schemes. Comparison of the numerical and analytical solutions indicate that, with proper treatment of the boundaries, very good agreement can be obtained. Comparison of numerical and experimental results shows that the assumption of hydrostatic pressure distribution imposes restrictions on the utility of the shallow‐water equations to represent the steady, supercritical flow. However, it appears that the basic features of many practical problems may be simulated using the procedures presented herein.

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