Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Particle velocity based hydrofracturing algorithm for a penny-shaped
  crack   A universal particle velocity based algorithm for simulating hydraulic
fracture with leak-off, previously demonstrated for the PKN and KGD models, is
extended to obtain solutions for a penny-shaped crack. The numerical scheme is
capable of dealing with both the viscosity and toughness dominated regimes,
with the fracture being driven by a power-law fluid. The computational approach
utilizes two dependent variables; the fracture aperture and the reduced
particle velocity. The latter allows for the application of a local condition
of the Stefan type (the speed equation) to trace the fracture front. The
obtained numerical solutions are carefully tested using various methods, and
are shown to achieve a high level of accuracy. Simple, accurate,
semi-analytical approximations of the solution are provided for the zero
leak-off case. A comparison with other results available in the literature is
undertaken.

5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas