On the gravity source term approximation for viscoplastic thin-layer models
Year: 2025
Type: article
Abstract: 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.
Source: Applied Mathematical Modelling
Authors: David K. Muchiri, Mathieu Sellier
Institution: University of Canterbury
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,510
OpenAlex ID: W4417516138