In this study, the numerical accuracy of porous shallow flow simulations through emergent vegetation is improved via flux reconstruction within the framework of the depth-averaged shallow water equations (SWEs). The model adopts a cell-centered finite volume (CCFV) method, where a new approach is applied to the flux reconstruction at cell interfaces using a third-order Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) method to capture smooth features effectively. We adopt the Koren flux limiter to reduce spurious oscillations, which is of third-order accuracy for sufficiently smooth data. Special attention is also given to the treatment of fluxes at boundaries, particularly wall and inflow conditions, to maintain third-order accuracy across the domain, without the explicit formulation of fictitious cells. Vegetation effects are represented through a new depth-integrated formulation for non-equilibrium conditions to evaluate the base component of drag force expression, water surface variations, and pressure gradient, and incorporated semi-implicitly together with the bed friction terms in the momentum equations. The model is validated against experimental data of steady flows through emergent vegetation with varying densities from sparse to dense, and demonstrates improved accuracy in predicting velocity streamwise profiles compared to conventional first- and second-order schemes, especially with coarser meshes. These results offer a valuable basis for extending modeling applications toward enhanced predictive accuracy.
Ginting et al. (Thu,) studied this question.