A wetting and drying treatment for the RungeKutta discontinuous Galerkin solution to the shallow water equations
This paper proposes a wetting and drying treatment for the piecewise linear RungeKutta discontinuous Galerkin approximation to the shallow water equations. The method takes a fixed mesh approach as opposed to mesh adaptation techniques and applies a post-processing operator to ensure the positivity of the mean water depth within each finite element. In addition, special treatments are applied in the numerical flux computation to prevent an instability due to excessive drying. The proposed wetting and drying treatment is verified through comparisons with exact solutions and convergence rates are examined. The obtained orders of convergence are close to or approximately equal to 1 for solutions with discontinuities and are improved for smooth solutions. The combination of the proposed wetting and drying treatment and a TVB slope limiter is also tested and is found to be applicable on condition that they are applied exclusively to an element at the same RungeKutta step.
wetting and drying shallow water equations moving boundary discontinuous galerkin method rkdg method