@Article{FernandezNieto2011,
  author   = {Fern{\'a}ndez Nieto, E. D. and Castro D{\'i}az, Manuel J. and Par{\'e}s, Carlos},
  journal  = {Journal of Scientific Computing},
  title    = {{O}n an {I}ntermediate {F}ield {C}apturing {R}iemann {S}olver {B}ased on a {P}arabolic {V}iscosity {M}atrix for the {T}wo-{L}ayer {S}hallow {W}ater {S}ystem},
  year     = {2011},
  number   = {1},
  pages    = {117-140},
  volume   = {48},
  abstract = {The goal of this article is to design a new approximate Riemann solver for the two-layer shallow water system which is fast compared to Roe schemes and accurate compared to Lax-Friedrichs, FORCE, or GFORCE schemes (see Castro et al. in Math. Comput. 79:1427–1472, 2010 ). This Riemann solver is based on a suitable decomposition of a Roe matrix (see Toumi in J. Comput. Phys. 102(2):360–373, 1992 ) by means of a parabolic viscosity matrix (see Degond et al. in C. R. Acad. Sci. Paris 1 328:479–483, 1999 ) that captures some information concerning the intermediate characteristic fields. The corresponding first order numerical scheme, which is called IFCP (Intermediate Field Capturing Parabola) is linearly L ∞ -stable, well-balanced, and it doesn’t require an entropy-fix technique. Some numerical experiments are presented to compare the behavior of this new scheme with Roe and GFORCE methods.},
  url      = {http://dx.doi.org/10.1007/s10915-011-9465-7},
}

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