Central-Upwind Schemes for Two-Layer Shallow Water Equations
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We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions are exactly preserved by the scheme and positivity preserving; that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new technique for the treatment of the nonconservative products describing the momentum exchange between the layers. The performance of the proposed method is illustrated on a number of numerical examples, in which we successfully capture (quasi) steady-state solutions and propagating interfaces. 2009 Society for Industrial and Applied Mathematics.
SIAM Journal on Scientific Computing
author list (cited authors)
Kurganov, A., & Petrova, G.
complete list of authors
Kurganov, Alexander||Petrova, Guergana