Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unified Asymptotic Preserving and Well-balanced Scheme for the Euler
  System with Multiscale Relaxation   The design and analysis of a unified asymptotic preserving (AP) and
well-balanced scheme for the Euler Equations with gravitational and frictional
source terms is presented in this paper. The asymptotic behaviour of the Euler
system in the limit of zero Mach and Froude numbers, and large friction is
characterised by an additional scaling parameter. Depending on the values of
this parameter, the Euler system relaxes towards a hyperbolic or a parabolic
limit equation. Standard Implicit-Explicit Runge-Kutta schemes are incapable of
switching between these asymptotic regimes. We propose a time
semi-discretisation to obtain a unified scheme which is AP for the two
different limits. A further reformulation of the semi-implicit scheme can be
recast as a fully-explicit method in which the mass update contains both
hyperbolic and parabolic fluxes. A space-time fully-discrete scheme is derived
using a finite volume framework. A hydrostatic reconstruction strategy, an
upwinding of the sources at the interfaces, and a careful choice of the central
discretisation of the parabolic fluxes are used to achieve the well-balancing
property for hydrostatic steady states. Results of several numerical case
studies are presented to substantiate the theoretical claims and to verify the
robustness of the scheme.

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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga