Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shock capturing and front tracking methods for granular avalanches   Shock formations are observed in granular avalanches when supercritical flow
merges into a region of subcritical flow. In this paper we employ a
shock-capturing numerical scheme for the one-dimensional Savage-Hutter theory
of granular flow to describe this phenomenon. A Lagrangian moving mesh scheme
applied to the non-conservative form of the equations reproduces smooth
solutions of these free boundary problems very well, but fails when shocks are
formed. A non-oscillatory central difference (NOC) scheme with TVD limiter or
WENO cell reconstruction for the conservative equations is therefore
introduced. For the avalanche free boundary problems it must be combined with a
front-tracking method, developed here, to properly describe the margin
evolution. It is found that this NOC scheme combined with the front-tracking
module reproduces both the shock wave and the smooth solution accurately. A
piecewise quadratic WENO reconstruction improves the smoothness of the solution
near local extrema. The schemes are checked against exact solutions for (1) an
upward moving shock wave, (2) the motion of a parabolic cap down an inclined
plane and (3) the motion of a parabolic cap down a curved slope ending in a
flat run-out region, where a shock is formed as the avalanche comes to a halt.

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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg