A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
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We consider a particular viscous shallow water model with topography and friction laws, formally derived by asymptotic expansion from the three-dimensional free surface Navier-Stokes equations. Emphasize is put on the numerical study: the viscous system is regarded as an hyperbolic system with source terms and discretized using a second order finite volume method. New steady states solutions for open channel flows are introduced for the whole model with viscous and friction terms. The proposed numerical scheme is validated against these new benchmarks.