Effective extension of a finite difference model for the solution of the shallow water equations to handle rapidly-varied, transcritical flows is presented, based on a semi-implicit, non-directional, operator splitting formulation on a staggered grid. Accuracy is preserved for smooth flows using the explicit, fully conser-vative, MOSQUITO scheme for momentum advection. Implicit formulation of 2D gravity wave propagation results in an elliptic problem which is efficiently solved by the preconditioned conjugate gradient method. Supercritical flows, steep fronts and hydraulic jumps are treated using flux limiters in the advection step only. The model is not subjected to spurious flows occurring in still water nor to inconsistencies with fundamental properties of 1D steady flows affecting a number of existing models. Strict mass conservation and accurate wetting and drying makes it feasible using the computed results for stable scalar transport computations. Numerical solutions to test problems mainly representative of flood wave flows and to laboratory tests of dam break flows are presented.
Semi-implicit modelling of 2D rapidly-varied flows with transitions
BALZANO, ANDREA;
2009-01-01
Abstract
Effective extension of a finite difference model for the solution of the shallow water equations to handle rapidly-varied, transcritical flows is presented, based on a semi-implicit, non-directional, operator splitting formulation on a staggered grid. Accuracy is preserved for smooth flows using the explicit, fully conser-vative, MOSQUITO scheme for momentum advection. Implicit formulation of 2D gravity wave propagation results in an elliptic problem which is efficiently solved by the preconditioned conjugate gradient method. Supercritical flows, steep fronts and hydraulic jumps are treated using flux limiters in the advection step only. The model is not subjected to spurious flows occurring in still water nor to inconsistencies with fundamental properties of 1D steady flows affecting a number of existing models. Strict mass conservation and accurate wetting and drying makes it feasible using the computed results for stable scalar transport computations. Numerical solutions to test problems mainly representative of flood wave flows and to laboratory tests of dam break flows are presented.
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