Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Implementation of ADER Schemes for Euler and
  Magnetohydrodynamical Flows on Structured Meshes -- Comparison with
  Runge-Kutta Methods   ADER (Arbitrary DERivative in space and time) methods for the time-evolution
of hyperbolic conservation laws have recently generated a fair bit of interest.
The ADER time update can be carried out in a single step, which is desirable in
many applications. However, prior papers have focused on the theory while
downplaying implementation details. The purpose of the present paper is to make
ADER schemes accessible by providing two useful formulations of the method as
well as their implementation details on three-dimensional structured meshes. We
therefore provide a detailed formulation of ADER schemes for conservation laws
with non-stiff source terms in nodal as well as modal space along with useful
implementation-related detail. We also provide details for the efficient use of
ADER schemes in obtaining the numerical flux for conservation laws as well as
electric fields for divergence-free magnetohydrodynamics. An efficient
WENO-based strategy for obtaining zone-averaged magnetic fields from
face-centered magnetic fields in MHD is also presented.
  The schemes catalogued here have been implemented in the first author's
RIEMANN code. The speed of ADER schemes is shown to be almost twice as fast as
that of strong stability preserving Runge-Kutta time stepping schemes for all
the orders of accuracy that we tested.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci