Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nektar++: Design and implementation of an implicit, spectral/$hp$
  element, compressible flow solver using a Jacobian-free Newton Krylov
  approach   At high Reynolds numbers, the use of explicit in time compressible flow
simulations with spectral/$hp$ element discretization can become significantly
limited by time step. To alleviate this limitation we extend the capability of
the spectral/$hp$ element open-source software framework, Nektar++, to include
an implicit discontinuous Galerkin compressible flow solver. The integration in
time is carried out by a singly diagonally implicit Runge-Kutta method. The
non-linear system arising from the implicit time integration is iteratively
solved by the Jacobian-free Newton Krylov (JFNK) method. A favorable feature of
the JFNK approach is its extensive use of the explicit operators available from
the previous explicit in time implementation. The functionalities of different
building blocks of the implicit solver are analyzed from the point of view of
software design and placed in appropriate hierarchical levels in the C++
libraries. In the detailed implementation, the contributions of different parts
of the solver to computational cost, memory consumption, and programming
complexity are also analyzed. A combination of analytical and numerical methods
is adopted to simplify the programming complexity in forming the
preconditioning matrix. The solver is verified and tested using cases such as
manufactured compressible Poiseuille flow, Taylor-Green vortex, turbulent flow
over a circular cylinder at $\text{Re}=3900$ and shock wave boundary-layer
interaction. The results show that the implicit solver can speed-up the
simulations while maintaining good simulation accuracy.

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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
2
The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an