Assessing the Applicability of Boussinesq-Type Models for Steep Obstacle Flow Simulations

Boussinesq-type models improve hydrodynamic simulations by capturing nonhydrostatic effects, offering advantages over nonlinear shallow-water equations. However, their performance in rapidly varying flows over steep beds remains unclear. This study evaluates the Serre–Green–Naghdi (SGN) model using a Gaussian hump test, with OpenFOAM serving as the Reynolds-averaged Navier–Stokes-based benchmark. Simulations were conducted for varying shallowness parameters, ϵ, defined as the ratio of energy head to hump curvature radius. Results show the SGN model performs well for ϵ<1 and moderately well up to a critical value ϵc when higher-order terms are included. Beyond ϵc, significant errors emerge—most notably, overpredicted pressure drops and underestimated discharge due to centrifugal effects. Flow field analysis reveals that while upstream velocity is improved with higher-order Boussinesq terms, downstream inaccuracies arise from neglected vortex dynamics. Flow separation and vortex formation at the crest are key contributors, exacerbated by bed friction, which lowers ϵc. These findings suggest limitations of irrotational Boussinesq frameworks for steep-bed flows and underscore the need to incorporate rotational effects for accurate modeling.