Modelling of coastal long-wave dynamics on unstructured mixed meshes under strong nonlinearity and pronounced baroclinity

Numerical modelling of coastal zone dynamics provides basis for solving a wide range of hydrogeological, engineering and ecological problems. A novel three-dimensional unstructured-mesh model is applied to simulate the dynamics of the density field and turbulence characteristics. The model is based on a finite-volume discretization and works on mixed unstructured meshes composed of triangles and quads. Although triangular meshes are most flexible geometrically, quads are more efficient numerically and do not support spurious inertial modes of triangular cell-vertex discretization. Mixed meshes composed of triangles and quads combine benefits of both. In particular, triangular transitional zones can be used to join quadrilateral meshes of differing resolution. The main aspects of this approach determining its reliability are discussed. The results of several simulations showing the performance of the model with respect to modelling wetting and drying, internal waves, and tidal dynamics are presented