On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System. Fernández-Nieto, E. D., Castro-Díaz, M. J., & Parés, C. Journal of Scientific Computing, 48(1):117-140, Jul, 2011.
On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System [link]Paper  doi  abstract   bibtex   
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 8-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.
@Article{FernandezNieto2011,
author= {Fern\'andez-Nieto, E. D. 
and Castro-D\'iaz, M. J. 
and Par\'es, C.},
title={On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System},
journal={Journal of Scientific Computing},
year={2011},
month={Jul},
day={01},
url_Paper = {http://hdl.handle.net/11441/32922},
volume={48},
number={1},
pages={117-140},
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 8-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.},
issn={1573-7691},
doi={10.1007/s10915-011-9465-7},

}

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