Shallow Water and Sediment Transport with Kelvin–Voigt Seabed: Numerical Insights from Theoretical Case Studies

Coastal erosion is increasingly influenced by anthropogenic alterations to the sediment cycle and morphological transformations. Traditional shallow water models often neglect the mechanical behavior of the seabed and its rheological response to hydrodynamic forcing, limiting their accuracy in forecasting erosion patterns. To address these limitations, this study extends the classical one-dimensional Saint-Venant (shallow water) model by incorporating effects of viscosity, frictional effects, sediment transport and viscoelasticity. The seabed is treated as a Kelvin–Voigt material, characterized by an elastic modulus and a viscous damping coefficient, to account for both immediate and time-dependent mechanical responses. Using the COMSOL Multiphysics platform, the evolution of the water column and seabed was simulated in six idealized case studies under various conditions, including changes in seabed topography and different frictional and dispersive regimes. The results demonstrate the influence of seabed topography, friction Sf, diffusion/dispersion regularization term E, and viscoelastic properties on wave seabed interactions and morphodynamic bed evolution (Exner-type). The inclusion of viscoelastic damping contributes to the stabilization of morphological evolution, mitigating abrupt changes in bathymetry and enhancing the physical realism of the simulations. The whole research aims to improve the prediction capabilities of erosion processes and advance the current modeling tools.