A review on advanced numerical methods for free-surface hydrodynamics

Abstract

Environmental hydrodynamics is typically characterized by free-surface hydrostatic flows. Within such a framework a set of simplified models are derived from the Reynolds averaged Navier–Stokes equations under various simplifying assumptions. Numerically, a simple method for the 1D open channel flow is derived first. This method is then extended to the $$2D_{xz}$$ 2 D xz laterally averaged model and to the $$2D_{xy}$$ 2 D xy vertically averaged model. Next, a semi-implicit method for the 3D model is described and discussed.