In this paper, a second order space discontinuous Galerkin (DG) method is presented for the numerical solution of inviscid shallow water flows over varying bottom topography. Novel in the implementation is the use of HLLC and kinetic numerical fluxes 1 in combination with a dissipation operator, applied only locally around discontinuities to limit spurious numerical oscillations. Numerical solutions over (non-)uniform meshes are verified against exact solutions; the numerical error in the L 2 -norm and the convergence of the solution are computed. Bore-vortex interactions are studied analytically and numerically to validate the model; these include bores as "breaking waves" in a channel and a bore traveling over a conical and Gaussian hump. In these complex numerical test cases, we correctly predict the generation of potential vorticity by non-uniform bores. Finally, we successfully validate the numerical model against measurements of steady oblique hydraulic jumps in a channel with a contraction. In the latter case, the kinetic flux is shown to be more robust.

Abstract:The problem of quantifying the effects of flexible plants on flow resistance and eddy viscosity by vegetated floodplains is first addressed with a one-dimensional (1D) approximation based upon the so-called lateral distribution method. The estimates so obtained are then tested with two-dimensional (2D) numerical simulations based on the full shallow water equations through the use of the computational code Telemac-2D. Data obtained on a physical model of the Besòs River (Spain), whose floodplains were covered with plastic ornamental plants to mimic the effect of flexible vegetation, is used for the validation of the numerical results. Additionally, the values of flow resistance estimated numerically with the 1D and 2D simulations are compared with values obtained in a rectangular flume under flow conditions (slope, water depth and artificial lining) similar to those used on the reduced model. It is then established that as more physical mechanisms are included in the mathematical model used to study the problem, the ratio between the floodplain and the main channel flow resistance coefficient increases. The approach demonstrates that whenever enough flow data is available, the lateral distribution method delivers values of flow resistance and eddy viscosity which are highly consistent with 2D numerical modelling. This finding could mean considerable savings in the burdensome task of specifying flow resistance and turbulence dissipation values for 2D modelling of large compound channel systems.

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