Semi‐implicit Skew Upwind Method for problems in environmental hydraulics

A new computational method is presented for reducing numerical diffusion in environmental fluid problems. This method, which is referred to as the Semi‐Implicit Skew Upwind Method (SISUM), is a robust solution procedure for the conditional convergence of the discretized transport equations. The method retains the advantage of the low numerical diffusion of the conventional skew upwind schemes but does not suffer from over‐ or under‐shooting often found in these methods due to the improved interpolation schemes. The effectiveness of SISUM is demonstrated in several examples. The comparison of the results of a hybrid scheme and SISUM with field observations of convection‐dominated pollutant transport in strongly curvilinear river flow shows that SISUM successfully eliminates the high numerical diffusion produced by the hybrid scheme. The robustness of the method was tested by solving the hydrodynamics of a circular clarifier model with a large density gravity source term in the vertical‐momentum equation.