An efficient scheme on wet/dry transitions for shallow water equations with friction
The present work concerns the derivation of a suitable discretization to approximate the friction source terms in the shallow-water model. Such additional source terms are known to be very stiff as soon as the water height is vanishing. The proposed numerical procedure comes from a relevant correction of a Godunov-type scheme that approximates the solutions of hyperbolic systems of conservation laws. The adopted correction gives a discretization of the source term which preserves the robustness and does not change the CFL condition. The scheme is shown to be particularly efficient for wet/dry transition simulations. in addition, this numerical procedure can be used together with any robust and well-balanced discretization of the topography source term. Second order extension is also investigated. Extensive numerical validations illustrate the interest of this new approach. (C) 2011 Elsevier Ltd. All rights reserved.
friction source term godunov-type schemes shallow-water equations hydrostatic reconstruction