  ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for
solving systems of first-order hyperbolic partial differential equations
(PDEs). Hyperbolic PDEs are typically derived from the conservation laws of
physics and are useful in a wide range of application areas. Applications
powered by ExaHyPE can be run on a student's laptop, but are also able to
exploit thousands of processor cores on state-of-the-art supercomputers. The
engine is able to dynamically increase the accuracy of the simulation using
adaptive mesh refinement where required. Due to the robustness and shock
capturing abilities of ExaHyPE's numerical methods, users of the engine can
simulate linear and non-linear hyperbolic PDEs with very high accuracy. Users
can tailor the engine to their particular PDE by specifying evolved quantities,
fluxes, and source terms. A complete simulation code for a new hyperbolic PDE
can often be realised within a few hours - a task that, traditionally, can take
weeks, months, often years for researchers starting from scratch. In this
paper, we showcase ExaHyPE's workflow and capabilities through real-world
scenarios from our two main application areas: seismology and astrophysics.
