Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An adaptive well-balanced positivity preserving central-upwind scheme on
  quadtree grids for shallow water equations   We present an adaptive well-balanced positivity preserving central-upwind
scheme on quadtree grids for shallow water equations. The use of quadtree grids
results in a robust, efficient and highly accurate numerical method. The
quadtree model is developed based on the well-balanced positivity preserving
central-upwind scheme proposed in [A. Kurganov and G. Petrova, Commun. Math.
Sci., 5 (2007), pp. 133--160]. The designed scheme is well-balanced in the
sense that it is capable of exactly preserving "lake-at-rest" steady states. In
order to achieve this as well as to preserve positivity of water depth, a
continuous piecewise bilinear interpolation of the bottom topography function
is utilized. This makes the proposed scheme capable of modelling flows over
discontinuous bottom topography. Local gradients are examined to determine new
seeding points in grid refinement for the next timestep. Numerical examples
demonstrate the promising performance of the central-upwind quadtree scheme.

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The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int