Explicit Methods for 2‐D Transient Free Surface Flows

MacCormack and Gabutti explicit finite‐difference schemes are introduced to integrate the equations describing two‐dimensional, unsteady gradually varied flows. Both schemes are second‐order accurate in space and time, allow sharp discontinuous initial conditions, and do not require isolation of the bores. Both sub‐ and supercritical flows may be present simultaneously in different parts of the channel or in a sequence in time. The inclusion of boundaries and stability conditions and the addition of artificial viscosity to smooth high‐frequency oscillations are discussed. To illustrate application of the schemes in hydraulic engineering, two typical problems are solved and the results of different schemes are compared.