Recent Advances in Numerical Methods for Hyperbolic PDE Systems

lt;p> Carlos Parés is a Professor of Applied Mathematics at the University of Málaga (Spain). He is a specialist in numerical methods for nonlinear hyperbolic systems of partial differential equations. He promoted the creation and development of the EDANYA group of research, which is currently an international reference in the simulation of geophysical flows. He was among the promoters of the series of conferences Numerical Methods for Hyperbolic Problems that started in 2009 in Castro-Urdiales (Spain).

María Luz Muñoz Ruiz is an Associate Professor in Applied Mathematics at the University of Málaga (Spain), from which she received an M.S. and Ph.D. degrees in Mathematics. She belongs to the Differential Equations, Numerical Analysis and Applications (EDANYA) research group, whose interests focus on the numerical resolution of nonconservative hyperbolic systems and its application to the simulation of geophysical flows.

Part I: Numerical methods for general problems.- 1 J.M. Gallardo et al., Incomplete Riemann solvers based on functional approximations to the absolute value function.- 2 M. Frank et al., Entropy-based methods for uncertainty quantification of hyperbolic conservation laws.- 3 I. Gomez Bueno et al., Well-balanced reconstruction operator for systems of balance laws: numerical implementation.- 4 V. Michel-Dansac and A. Thomann, On high-precision L?-stable IMEX schemes for scalar hyperbolic multi-scale Equations.- Part II: Numerical methods for speci_c problems.- 5 D. Grapsas et al., A staggered preassure correction numerical scheme to compute a travellimg reactive interface in a partially premixed mixture.- 6 M. Lukacova et al., New Invariant Domain Preserving Finite Volume Schemes for Compressible Flows.- 7 S. Jöns et al., Recent Advances and Complex Applications of the Compressible Ghost-Fluid Method.- 8 J. P. Berberich and C. Klingenberg, Entropy Stable Numerical Fluxes for CompressibleEuler Equations which are Suitable for All Mach Numbers.- 9 P. Poullet et al., Residual based method for sediment transport.- Part III: New ow models.- 10 B. B. Dhia et al., Pseudo-compressibility, dispersive model and acoustic waves in shallow water flows.- 11 M. Ali Debyaoui and M. Ersoy, A Generalised Serre-Green-Naghdi equations for variable rectangular open channel hydraulics and its finite volume approximation.