On the gravity source term approximation for viscoplastic thin-layer models

• A simple hybrid gravity source term is proposed for viscoplastic thin-layer models • The hybrid term incorporates both topographic slope and surface height gradients • Improves prediction of front positions and free-surface profiles in dam-break flows • Demonstrates better agreement with experiments than classical slope-based models • Applicable to both lubrication and shallow water equations across slope regimes The ability of thin-layer models to produce physically correct flow solutions in the acceleration, deceleration, and stopping phase is very crucial for industrial and geophysical applications. In this work, we propose a simple hybrid approximation of the gravity source term for the lubrication approximation and the shallow water equations, aimed at preventing the overestimation of front positions in dam-break-type flows. The proposed formulation incorporates contributions from both the topographic slope and the free-surface height gradients, offering a more balanced representation of gravitational forcing across different regions of the flow domain. This is particularly important for yield stress fluids, whose motion depends on gravity-induced stresses exceeding a critical yield threshold. The proposed model allows better prediction of the free-surface profile in the tip and rear regions for both shallow and steep inclinations. We observe excellent agreements with experiments compared to existing numerical solutions in the literature, which rely solely on classical slope-driven gravity terms.