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Hydromagnetic turbulence in computer simulations. (English) Zbl 1016.85002
Summary: The usefulness of high-order schemes in astrophysical MHD turbulence simulations is discussed. Simple advection tests of hat profiles are used to compare schemes of different order. Higher order schemes generally need less explicit diffusion. In the case of a standing Burgers shock it is shown that the overall accuracy improves as the order of the scheme is increased. A memory efficient 3-step $$2N$$-RK scheme is used. For cache efficiency, the entire set of equations is solved along pencils in the $$yz$$-plane. The advantage of solving for the magnetic vector potential is highlighted. Finally, results from a simulation of helical turbulence exhibiting large scale dynamo action are discussed.

##### MSC:
 85-08 Computational methods for problems pertaining to astronomy and astrophysics 85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics 76F99 Turbulence 76M25 Other numerical methods (fluid mechanics) (MSC2010)
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##### References:
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