Mathematical modelling and simulation of Shallow Water flows of viscoplastic fluids

par David Muchiri

mardi 24 oct. 2023, 11:15 → 12:15 Europe/Paris

Amphi Schwartz (IMT)

We present mathematical modelling and simulation of thin free surface flows of viscoplastic fluids (like lava and mud flows) with a Herschel-Bulkley rheology. Using asymptotic expansion method, depth-integrated models (lubrication and shallow water type models) are derived for three-dimensional multi-regime flows on non-flat inclined topographies with varying basal conditions. Starting from the reference solutions (zeroth-order ones), flow models are calculated as perturbations of these reference solutions. Two flow regimes corresponding to different balances between shear and pressure forces are presented. The classical flow models in the literature (corresponding to the first regime) are recovered by considering their respective cases on a flat-inclined surface. Computed results are compared with experimental data from the literature and are found to be in good agreement.