Application of a Discontinuous Galerkin Method to 1-D Liquid Sloshing

A discontinuous Galerkin method is applied to the shallow water equations written in a rotating frame of reference. Linear approximating functions are employed on each element. A minmod slope limiter is incorporated to ensure non-linear total variation bounded (TVB) stability. The method is first applied to the dam breaking problem with zero rotation to validate the numerical implementation. A rotating tank is then investigated with sinusoidal rotation. Results are computed with and without slope limiting to investigate the effect of slope limiting on the solution. The DG method is also compared to a first order Godunov method and to experimental data.