Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fifth order finite volume WENO in general orthogonally-curvilinear
  coordinates   High order reconstruction in the finite volume (FV) approach is achieved by a
more fundamental form of the fifth order WENO reconstruction in the framework
of orthogonally-curvilinear coordinates, for solving the hyperbolic
conservation equations. The derivation employs a piecewise parabolic polynomial
approximation to the zone averaged values to reconstruct the right, middle, and
left interface values. The grid dependent linear weights of the WENO are
recovered by inverting a Vandermode-like linear system of equations with
spatially varying coefficients. A scheme for calculating the linear weights,
optimal weights, and smoothness indicator on a regularly- and
irregularly-spaced grid in orthogonally-curvilinear coordinates is proposed. A
grid independent relation for evaluating the smoothness indicator is derived
from the basic definition. Finally, the procedures for the source term
integration and extension to multi-dimensions are proposed. Analytical values
of the linear and optimal weights, and also the weights required for the source
term integration and flux averaging, are provided for a regularly-spaced grid
in Cartesian, cylindrical, and spherical coordinates. Conventional fifth order
WENO reconstruction for the regularly-spaced grids in the Cartesian coordinates
can be fully recovered in the case of limiting curvature. The fifth order
finite volume WENO-C (orthogonally-curvilinear version of WENO) reconstruction
scheme is tested for several 1D and 2D benchmark test cases involving smooth
and discontinuous flows in cylindrical and spherical coordinates.

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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex