Simulating Turbulence Using the Astrophysical Discontinuous Galerkin Code TENET

In astrophysics, the two main methods traditionally in use for solving the Euler equations of ideal fluid dynamics are smoothed particle hydrodynamics and finite volume discretization on a stationary mesh. However, the goal to efficiently make use of future exascale machines with their ever higher degree of parallel concurrency motivates the search for more efficient and more accurate techniques for computing hydrodynamics. Discontinuous Galerkin (DG) methods represent a promising class of methods in this regard, as they can be straightforwardly extended to arbitrarily high order while requiring only small stencils. Especially for applications involving comparatively smooth problems, higher-order approaches promise significant gains in computational speed for reaching a desired target accuracy. Here, we introduce our new astrophysical DG code TENET designed for applications in cosmology, and discuss our first results for 3D simulations of subsonic turbulence. We show that our new DG implementation provides accurate results for subsonic turbulence, at considerably reduced computational cost compared with traditional finite volume methods. In particular, we find that DG needs about 1.8 times fewer Andreas Bauer • Rüdiger Pakmor Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany, e-mail: [email protected]; [email protected] Kevin Schaal • Volker Springel Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany, Zentrum für Astronomie der Universität Heidelberg, Astronomisches Recheninstitut, Mönchhofstr. 12-14, 69120 Heidelberg, Germany, e-mail: [email protected]; [email protected] Praveen Chandrashekar TIFR Centre for Applicable Mathematics, Bangalore-560065, India, e-mail: [email protected] Christian Klingenberg Institut für Mathematik, Universität Würzburg, Emil-Fischer-Str. 30, 97074 Würzburg, Germany, e-mail: [email protected]