Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient conservative ADER schemes based on WENO reconstruction and
  space-time predictor in primitive variables   We present a new version of conservative ADER-WENO finite volume schemes, in
which both the high order spatial reconstruction as well as the time evolution
of the reconstruction polynomials in the local space-time predictor stage are
performed in primitive variables, rather than in conserved ones. Since the
underlying finite volume scheme is still written in terms of cell averages of
the conserved quantities, our new approach performs the spatial WENO
reconstruction twice: the first WENO reconstruction is carried out on the known
cell averages of the conservative variables. The WENO polynomials are then used
at the cell centers to compute point values of the conserved variables, which
are converted into point values of the primitive variables. A second WENO
reconstruction is performed on the point values of the primitive variables to
obtain piecewise high order reconstruction polynomials of the primitive
variables. The reconstruction polynomials are subsequently evolved in time with
a novel space-time finite element predictor that is directly applied to the
governing PDE written in primitive form. We have verified the validity of the
new approach over the classical Euler equations of gas dynamics, the special
relativistic hydrodynamics (RHD) and ideal magnetohydrodynamics (RMHD)
equations, as well as the Baer-Nunziato model for compressible two-phase flows.
In all cases we have noticed that the new ADER schemes provide less oscillatory
solutions when compared to ADER finite volume schemes based on the
reconstruction in conserved variables, especially for the RMHD and the
Baer-Nunziato equations. For the RHD and RMHD equations, the accuracy is
improved and the CPU time is reduced by about 25%. We recommend to use this
version of ADER as the standard one in the relativistic framework. The new
approach can be extended to ADER-DG schemes on space-time adaptive grids.

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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn