High Resolution Well-Balanced Compact Implicit Numerical Scheme for Numerical Solution of the Shallow Water Equations

In this work, we solve the shallow water equations with topography using a novel high resolution well-balanced compact implicit finite difference scheme. The scheme uses the Lax–Friedrichs flux splitting method together with the fractional step and fast sweeping method. The values of the scheme’s parameters are set using the ENO method. The scheme is extended to have the well-balanced property for the lake at rest example following the procedure in [9]. In the section on numerical experiments, the accuracy of the scheme is shown.