Journal
COMPUTERS & FLUIDS
Volume 48, Issue 1, Pages 192-201Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.compfluid.2011.04.011
Keywords
Shallow-water equations; Friction source term; Godunov-type schemes; Hydrostatic reconstruction
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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.
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