Abstract
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 degrees of freedom to achieve the same accuracy and at the same time is more than 1.5 times faster, confirming its substantial promise for astrophysical applications.
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Notes
- 1.
We are using the convention of normalizing the Fourier transform symmetrically with (2π)−3∕2.
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Acknowledgements
We thank Gero Schnücke, Juan-Pablo Gallego, Johannes Löbbert, Federico Marinacci, Christoph Pfrommer, and Christian Arnold for very helpful discussions. The authors gratefully acknowledge the support of the Klaus Tschira Foundation. We acknowledge financial support through subproject EXAMAG of the Priority Program 1648 ‘SPPEXA’ of the German Research Foundation, and through the European Research Council through ERC-StG grant EXAGAL-308037. KS and AB acknowledge support by the IMPRS for Astronomy and Cosmic Physics at the Heidelberg University. PC was supported by the AIRBUS Group Corporate Foundation Chair in Mathematics of Complex Systems established in TIFR/ICTS, Bangalore.
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Bauer, A., Schaal, K., Springel, V., Chandrashekar, P., Pakmor, R., Klingenberg, C. (2016). Simulating Turbulence Using the Astrophysical Discontinuous Galerkin Code TENET. In: Bungartz, HJ., Neumann, P., Nagel, W. (eds) Software for Exascale Computing - SPPEXA 2013-2015. Lecture Notes in Computational Science and Engineering, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-40528-5_17
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DOI: https://doi.org/10.1007/978-3-319-40528-5_17
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