NumHyp19 is the sixth in a series of biannual conferences that began with a meeting in Castro Urdiales, Spain in 2009. Further editions of this conference were held in Roscoff, France in 2011, Aachen, Germany in 2013, Cortona, Italy in 2015, and Monte Verità, Switzerland in 2017. These conferences focus on recent developments and new directions in the area of numerical methods for hyperbolic and convection dominated partial differential equations (PDEs). These PDEs arise in a large number of models in physics and engineering. Prominent examples include the compressible and incompressible Euler and Navier-Stokes equations, the shallow water equations, the magneto-hydrodynamics equations, multiphase fluid models, etc. Example of application areas are aerodynamics, oceanography, plasma physics, solid mechanics...

These PDEs have been subjected to extensive analytical and numerical studies over the last decades. It is widely known that their solutions can exhibit very complex behavior including the presence of singularities such as shock waves, sensitive dependence to initial conditions, presence of multiple spatio-temporal scales, appearance of turbulent regimes, etc. The design and the analysis of numerical methods with good properties to solve them are still a challenge. 

The list of main topics of this edition include: