A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers

We present a novel staggered semi-implicit hybrid finite volume / element method for the numerical solution of shallow water equations at all Froude numbers on unstructured meshes. A semi-discretization in time conservative Saint-Venant with bottom friction terms leads to its decomposition into first order hyperbolic subsystem containing nonlinear convective term and second wave equation pressure. For spatial discretization free surface elevation an mesh composed triangular simplex elements is considered, whereas dual grid edge-type employed computation depth-averaged momentum vector. The stage proposed algorithm consists using explicit Godunov-type grid. Next, classical continuous scheme provides vertices primal mesh. strategy followed this paper circumvents contribution celerity CFL-type step restriction, hence making well-suited low number flows. It can be shown that limit reduces FV/FE projection incompressible Navier-Stokes equations. At same time, formulation governing also allows high flows shock waves. As such, new considered all-Froude solver, able deal simultaneously both, subcritical as well supercritical Besides, balanced by construction. accuracy overall methodology studied numerically C-property proven theoretically validated via experiments. several Riemann problems, including flat jumps, attests robustness bores discontinuities. Finally, 3D dam break problem over dry our results are successfully compared reference solutions obtained available experimental data.