Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-dimensional discontinuous Galerkin based high-order gas-kinetic
  scheme and GPU implementation   In this paper, the discontinuous Galerkin based high-order gas-kinetic
schemes (DG-HGKS) are developed for the three-dimensional Euler and
Navier-Stokes equations. Different from the traditional discontinuous Galerkin
(DG) methods with Riemann solvers, the current method adopts a kinetic
evolution process, which is provided by the integral solution of
Bhatnagar-Gross-Krook (BGK) model. In the weak formulation of DG method, a
time-dependent evolution function is provided, and both inviscid and viscous
fluxes can be calculated uniformly. The temporal accuracy is achieved by the
two-stage fourth-order discretization, and the second-order gas-kinetic solver
is adopted for the fluxes over the cell interface and the fluxes inside a cell.
Numerical examples, including accuracy tests and Taylor-Green vortex problem,
are presented to validate the efficiency and accuracy of DG-HGKS. Both optimal
convergence and super-convergence are achieved by the current scheme. The
comparison between DG-HGKS and high-order gas-kinetic scheme with weighted
essential non-oscillatory reconstruction (WENO-HGKS) is also given, and the
numerical performances are comparable with the approximate number of degree of
freedom. To accelerate the computation, the DG-HGKS is implemented with the
graphics processing unit (GPU) using compute unified device architecture
(CUDA). The obtained results are also compared with those calculated by the
central processing units (CPU) code in terms of the computational efficiency.
The speedup of GPU code suggests the potential of high-order gas-kinetic
schemes for the large scale computation.

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The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: stat