Semi-implicit Modelling of Rapidly Varied Flows with Transitions

BALZANO, ANDREA;E. TORRICELLI

2006-01-01

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Abstract

A two-dimensional, finite difference model for rapidly varied transcritical flows based on the semi-implicit, operator splitting formulation on staggered grid is presented. Unlike Eulerian-Lagrangian fractional step models, momentum advection is made fully conservative by use of the Eulerian, explicit, MOSQUITO scheme. The related stability condition on the velocity-based Courant number is fulfilled in the advection step only, thus taking advantage of the implicit structure of both the diffusion and the gravity wave propagation steps. Supercritical flows, steep fronts and hydraulic jumps are treated using the ULTIMATE flux limiter in the advection step and artificial viscosity. Computational solutions are presented to test problems mainly representative of flood wave flows and to laboratory tests of dam break flows.