Derivation and Numerical Resolution of 2D Shallow Water Equations for Multi-Regime Flows of Herschel-Bulkley Fluids

28 p.; This paper presents mathematical modeling and simulation of thin free surface flows of viscoplastic fluids with a Herschel-Bulkley rheology over complex topographies. Using asymptotic expansion method, depthaveraged 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. In the second regime case, a pressure term is non-negligible. Mathematically it leads to a corrective term to the classical regime equations. Using dimensionless parameters, the two regimes flow solutions are compared; the differences appear in the vicinity of sharp changes of slopes. Comparisons of numerical results with dam-break experiments in different geometries are presented for validation.