A slope modification method for shallow water equations

A slope modification method is proposed for non‐oscillatory schemes based on the Lax‐Friedrich solver. The modified scheme is proved to be total‐variation‐diminishing (TVD) and second‐order accurate. Application of the scheme to the shallow water equations produces sharp profiles for shocks and achieves high accuracy in the smooth regions of the solution. Copyright © 1992 John Wiley & Sons, Ltd