Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anti-diffusive, Non-oscillatory Central (adNOC) scheme to solve the
  shallow water equations over an erodible substrate in two dimensions   Shallow water surface flows commonly entrain sediments, resulting in scouring
and/or deposition of the underlying substrate that may strongly influence the
pattern of subsequent flow. These coupled phenomena, which can be investigated
mathematically with some extension of the shallow water equations, present
numerous challenges for numerical methods. Here, we present a straightforward
Riemann-solver free approach to solve these equations based on the explicit
non-oscillatory central (NOC) scheme that has already been widely applied to
hyperbolic conservation laws in other contexts. Our version of the central
scheme is second-order accurate in time and space and is used with an
anti-diffusive correction to reduce numerical diffusion usually suffered by
central schemes. Numerical experiments show that the scheme is accurate and
robust for a range of applications from highly dynamic spontaneous dam break
over a mobile bed to slowly evolving morphological bed in an alluvial river.

12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
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The categories of this paper are: stat
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph