The course starts with an introduction to common spatial and temporal discretization techniques to numerically solve sets of partial differential equations. Further on, the course treats various state-of-the-art numerical methods used in astrophysical computations. This encompasses basic shock-capturing schemes as employed in modern Computational Fluid Dynamics, common approaches for handling Radiative Transfer, and concrete gas dynamical applications with astrophysical counterparts. The main aim is to give insight in the advantages and disadvantages of the employed numerical techniques. The course will illustrate their typical use with examples which concentrate on stellar out-flows where the role and numerical treatment of radiative losses will be illustrated, but also touch on studies from solar physics, stellar atmospheres, astrophysical accretion disks and jets, pulsar winds, planetary nebulae, interacting stellar winds, supernovae . . . . The students will experiment with existing and/or self-written software, and gain hands-on insight in algorithms, their convergence rates, time step limitations, stability, .... The students will in the end be able to apply some of the schemes to selected test problems.
