Preface to the special issue “Recent Advances in Numerical Methods for Hyperbolic Partial Differential Equations”

Michael Dumbser, Gregor Gassner, Christian Rohde and Sabine Roller

Applied Mathematics and Computation, 2016, vol. 272, issue P2, 235-236

Abstract: Hyperbolic partial differential equations (PDE) are a very powerful mathematical tool to describe complex dynamic processes in science and engineering. Very often, hyperbolic PDE can be derived directly from first principles in physics, such as the conservation of mass, momentum and energy. These principles are universally accepted to be valid and can be used for the simulation of a very wide class of different problems, ranging from astrophysics (rotating gas clouds, the merger of a binary neutron star system into a black hole and the associated generation and propagation of gravitational waves) over geophysics (generation and propagation of seismic waves after an earthquake, landslides, avalanches, tidal waves, storm surges, flooding and morphodynamics of rivers) to engineering (turbulent flows over aircraft and the associated noise generation and propagation, rotating flows in turbo-machinery, multi-phase liquid-gas flows in internal combustion engines) and computational biology (blood flow in the human cardio-vascular system).

Keywords: Time-dependent hyperbolic partial differential equations; Conservation laws; Hyperbolic PDE with higher order derivatives; Hyperbolic PDE with non-conservative products; Friedrichs systems; Finite volume methods; Discontinuous Galerkin finite element methods; Well-balanced schemes; Riemann solvers; Computational hemodynamics; Turbulent flows and multi-phase flows (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:272:y:2016:i:p2:p:235-236

DOI: 10.1016/j.amc.2015.11.023

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