Depth-averaged coupling of submerged granular deformation with fluid flow: An augmented HLL scheme

Abstract

Debris flow in or towards water bodies, and bed load transport in open channels manifest from the interaction of fluid with deformable granular media at varied spatiotemporal scales. The present study aims to formulate a robust two-dimensional coupled depth-averaged framework for simulation of submarine deformation of non-cohesive granular media and the corresponding effect on water and the otherwise. The unified framework consisting of conditional hyperbolic set of partial differential equations has been conceptualized as two concurrent yet independent systems interacting through source/sink terms comprising of drag force, shear and water-surface gradient. The system is solved on a regular finite volume grid through a robust modification of the Harten-Lax-Van Leer (HLL) scheme. The interaction terms are embedded into the interfacial fluxes, where additional closure employs the effect of dry-wet zone transition and flow arrest for both modules. Various aspects of the proposed framework are validated against an array of test cases ranging from landslide induced tsunami to dambreak induced scour. The last representative scenario emphasizes the potential applicability of the model for real-time extension to field-scale problems. A few one-dimensional approximations are explored in the Appendix to calculate relative velocity between interstitial fluid and granular media for computation of drag force.