Recent Advances in Numerical Methods for Hyperbolic PDE Systems

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.

The volume is addressed to PhD students and researchers in Applied Mathematics, Fluid Mechanics, or Engineering whose investigation focuses on or uses numerical methods for hyperbolic systems. It may also be a useful tool for practitioners who look for state-of-the-art methods for flow simulation.

State-of-the-art numerical methods with good properties are presented Applications to many different flow models are shown including Euler and Navier-Stokes equations, multilayer and dispersive shallow water models, magnetohydrodynamics, multiphase flow, sediment transport, turbulent deflagrations, etc. The combination of rigorous numerical analysis and real-world applications may stimulate new successful developments of mathematical techniques to solve challenging problems

Autorentext

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.

Giovanni Russo is a full professor of numerical analysis at the University of Catania. Works on numerical methods for evolutionary partial differential equations, and other topics in computation and applied mathemastics. Author of more than a hundred papers on international journals. Associate editor of SIMA, CMS, and other journals, responsible for various national and international research projects, chair of several international conferences and workshops. Has been PhD coordinator for more than sixteen years.

Inhalt
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. <p