Evaluating the influence of slope limiters on nearshore wave simulation in a non-hydrostatic model

Abstract

Abstract In a non-hydrostatic model utilizing a Godunov-type finite volume method, the numerical dissipation introduced by slope limiters can be a main source of total dissipation. The objective of this study is to look into how different slope limiters influence nearshore wave simulation with an emphasis on depth-limited wave breaking simulation in the open-source NHWAVE model. The minmod, superbee and van Leer limiter are analyzed. The performances of different slope limiters are correlated with their characteristics. The refinement of the grids do not necessarily help to improve the model accuracy. In the shock-capturing modeling of solitary waves, although superbee limiter introduces a small non-physical increase of wave energy before wave breaking, the overall dissipation is largest. The van Leer limiter does not introduce noticeable dissipation before breaking in a relatively short simulation time, and the energy dissipated is moderate of all three limiters. In the turbulent modeling of wave breaking, slope limiters do not introduce large numerical dissipation and the model accuracy is mainly influenced by the dissipation in wave propagation and generating turbulent dissipation at different orders of magnitude. The superbee limiter predicts the largest turbulent kinetic energy at breaking moment, which means superbee limiter tends to reproduce the most intensive breaking. It is consistent with the largest wave energy dissipation in the shock-capturing modeling.