Interface problems have many applications. Mathematically, interface problems usually lead
to differential equations whose input data and solutions are non-smooth or discontinuous …

An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and
magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive …

Interface problems arise in many applications. For example, when there are two different
materials, such as water and oil, or the same material but at different states, such as water …

Numerical modelling of transoceanic tsunami propagation, together with the detailed
modelling of inundation of small-scale coastal regions, poses a number of algorithmic …

Many geophysical flow or wave propagation problems can be modeled with two-
dimensional depth-averaged equations, of which the shallow water equations are the …

We evaluate a new depth-averaged mathematical model that is designed to simulate all
stages of debris-flow motion, from initiation to deposition. A companion paper shows how …

In the first edition, we paid attention not only to tsunami waves, but to related phenomena,
namely, seaquakes, as well, which to a significant extent reflected the interests of the …

The approximation of transient detonation waves requires numerical methods that are able
to resolve a wide range of different scales. Especially the accurate consideration of detailed …

We present the first high order one-step ADER-WENO finite volume scheme with adaptive
mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is …

A simple interface-capturing approach proposed previously by the author for efficient
numerical resolution of multicomponent problems with a van der Waals fluid [J. Comput …