Explicit numerical schemes for unsteady free‐surface flows with shocks

Three second‐order accurate, explicit finite‐difference schemes (MacCormack, Lambda, and Gabutti) are introduced and compared for the analysis of unsteady, free‐surface flows having shocks or bores. The details of these schemes, their shock‐capturing capabilities, stability restrictions, boundary conditions, and use of artificial viscosity to dampen the numerical oscillations near the shock are presented. Computed results are compared with the analytical solution to demonstrate their validity. A comparison of the computer time required for reproducing the shocks with a similar accuracy shows that the Preissmann's implicit scheme takes four to eight times the CPU time taken by these explicit schemes. Because the latter are easier to program, it makes them attractive for real‐life applications.