Abstract

I was invited to give a sequence of six lectures at the 2016 Les Houches Summer School on Computational Astrophysics. Each lecture is one and a half hours long and is split into two or three parts. The goal of my set of lectures is to give students a "from the inside out" understanding of astrophysical fluid and magnetofluid dynamical codes. In other words, these codes tend to be very difficult to understand from the outside-in. However, if one understands just a little about the core algorithms that make these codes work, one arrives at an inside-out understanding of the codes. Consequently, one understands which algorithms go into the codes and, therefore, what the codes are doing. This makes it very easy to understand the codes. This quick introduction, via six video lectures, will get the viewer properly oriented with many of the important algorithms that are used in astrophysics codes. The slides that go along with the codes are also available.

Because of the summer-school format, it was possible to design a set of exercises with increasing complexity that were properly keyed to the lectures. There is one set of computer exercises that is keyed to each of the first four lectures. The numerical codes in these exercises are self- documenting and README files are included. This should give the viewer some orientation with respect to the tasks in the exercises. The distribution includes worked examples.

The last two lectures give a modern perspective on higher order schemes and multidimensional Riemann solvers that make it possible to have divergence-free MHD. For that reason, the exercises associated with the last two lectures constitute the author's RIEMANN code itself. Two versions of this code are provided. The first version is a second order scheme for astrophysical hydrodynamics and MHD. The second version is a larger code that supports second, third and fourth order accurate algorithms. At second order, one can choose between TVD or WENO reconstruction. At third order, one can choose between PPM and third order WENO reconstruction. At fourth order, the only choice is WENO reconstruction. In each instance, space-time accuracy is achieved via ADER methods. Fluxes and electric fields are evaluated using several advanced one-dimensional and multidimensional Riemann solvers. The full code distribution includes numerous worked examples of astrophysical applications.

HAPPY COMPUTING!!

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