The present volume contains selected papers issued from the sixth edition of the International Conference "Numerical methods for hyperbolic problems" that took place in 2019 in Málaga (Spain). NumHyp conferences, which began in 2009, focus on recent developments and new directions in the field of numerical methods for hyperbolic partial differential equations (PDEs) and their applications. The 11 chapters of the book cover several state-of-the-art numerical techniques and applications, including the design of numerical methods with good properties (well-balanced, asymptotic-preserving, high-order accurate, domain invariant preserving, uncertainty quantification, etc.), applications to models issued from different fields (Euler equations of gas dynamics, Navier-Stokes equations, multilayer shallow-water systems, ideal magnetohydrodynamics or fluid models to simulate multiphase flow, sediment transport, turbulent deflagrations, etc.), and the development of new nonlinear dispersive shallow-water models.

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.