Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-implicit Hybrid Discrete $\left(\text{H}^T_N\right)$ Approximation
  of Thermal Radiative Transfer   The thermal radiative transfer (TRT) equations form an integro-differential
system that describes the propagation and collisional interactions of photons.
Computing accurate and efficient numerical solutions TRT are challenging for
several reasons, the first of which is that TRT is defined on a
high-dimensional phase. In order to reduce the dimensionality of the phase
space, classical approaches such as the P$_N$ (spherical harmonics) or the
S$_N$ (discrete ordinates) ansatz are often used in the literature. In this
work, we introduce a novel approach: the hybrid discrete (H$^T_N$)
approximation to the radiative thermal transfer equations. This approach
acquires desirable properties of both P$_N$ and S$_N$, and indeed reduces to
each of these approximations in various limits: H$^1_N$ $\equiv$ P$_N$ and
H$^T_0$ $\equiv$ S$_T$. We prove that H$^T_N$ results in a system of hyperbolic
equations for all $T\ge 1$ and $N\ge 0$. Another challenge in solving the TRT
system is the inherent stiffness due to the large timescale separation between
propagation and collisions, especially in the diffusive (i.e., highly
collisional) regime. This stiffness challenge can be partially overcome via
implicit time integration, although fully implicit methods may become
computationally expensive due to the strong nonlinearity and system size. On
the other hand, explicit time-stepping schemes that are not also
asymptotic-preserving in the highly collisional limit require resolving the
mean-free path between collisions, making such schemes prohibitively expensive.
In this work we develop a numerical method that is based on a nodal
discontinuous Galerkin discretization in space, coupled with a semi-implicit
discretization in time. We conduct several numerical experiments to verify the
accuracy, efficiency, and robustness of the H$^T_N$ ansatz and the numerical
discretizations.

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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: hep-lat