Refinement indicator for mesh adaption in shallow-water modeling

Automatic mesh refinement can create suitable resolution for a hydrodynamic simulation in a computationally efficient manner. Development of an automatic adaptive procedure will rely on estimating and/or controlling computational error by adapting the mesh parameters with respect to a particular measurement. Since a primary source of error in a discrete approximation of the shallow-water equations is inadequate mesh resolution, an adaptive mesh can be an efficient approach to increase accuracy. This paper introduces a simple indicator for the shallow water equations that measures the error in a norm of mass conservation to determine which elements require refinement or coarsening. The resulting adaptive grid gives results comparable to a much higher resolution (uniformly refined) mesh with less computational expense.