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. © ASCE.