Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A MacCormack Method for Complete Shallow Water Equations with Source
  Terms   In the last decades, more or less complex physically-based hydrological
models, have been developed to solve the shallow water equations or their
approximations using various numerical methods. The MacCormack method was
developed for simulating overland flow with spatially variable infiltration and
microtopography using the hydrodynamic flow equations. The basic MacCormack
scheme is enhanced when it uses the method of fractional steps to treat the
friction slope or a stiff source term and to upwind the convection term in
order to control the numerical oscillations and stability. In this paper we
describe, the MacCormack scheme for 1D complete shallow water equations with
source terms, analyze the stability condition of the method and we provide the
convergence rate of the algorithm. This work improves some well known results
deeply studied in the literature which concern the Saint-Venant problem and it
represents an extension of the time dependent shallow water equations without
source terms. The numerical evidences consider the rate of convergence of the
method and compares the numerical solution respect to the analytical one.

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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph