Solution-adaptivity in modelling complex shallow flows

A solution-adaptive algorithm is presented and tested for the shallow water equations. Specifically, we focus on the two-dimensional modelling of wind-induced hydrodynamics in shallow waters, characterised by a strong influence of variable bed topography and aquatic vegetation. The numerical solution is obtained using a Godunov-type finite-volume scheme on a hierarchical Cartesian mesh, with local time stepping. A simple, but robust algorithm based on the velocity gradient is proposed to control the dynamic mesh adaptation. Simulations on a representative steady-state and unsteady benchmark problem show that solution-adaptivity is successful in reallocating cells to where they improve global accuracy more efficiently. The algorithm is then applied to model the wind-driven circulations in Lake Neusiedl, proving the algorithm’s robustness in resolving complex geometry and vegetation cover.