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High-Order Implicit Hybridizable Discontinuous Galerkin Method for the Boltzmann Equation

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Wei Su, Peng Wang, Yonghao Zhang, Lei Wu

Fluid Dynamics · Submitted 19 Jul 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The proposed scheme is proved to be accurate and efficient.

how it is stated · asserted 1.00 read the record →

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arXiv ID1807.07644 (version 1)
Pith IDKRQSJ4OV, Pith's permanent record of this paper and its review
CitationLei Wu, Peng Wang, Wei Su, Yonghao Zhang. "High-Order Implicit Hybridizable Discontinuous Galerkin Method for the Boltzmann Equation." arXiv:1807.07644 (2018). https://pith.science/paper/KRQSJ4OV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,185 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular meshes. The velocity distribution function and its trace are approximated in the piecewise polynomial space of degree up to 4. The fast spectral method (FSM) is incorporated into the DG discretization to evaluate the collision operator. Specific polynomial approximation is proposed for the collision term to reduce the computational cost. The proposed scheme is proved to be accurate and efficient.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular meshes. method 0.72 0.89 0.12 asserted 1.00
s1 The velocity distribution function and its trace are approximated in the piecewise polynomial space of degree up to 4. method 0.99 0.85 0.03 asserted 1.00
s2 The fast spectral method (FSM) is incorporated into the DG discretization to evaluate the collision operator. method 0.97 0.75 0.04 asserted 1.00
s3 Specific polynomial approximation is proposed for the collision term to reduce the computational cost. method 0.73 0.86 0.07 asserted 0.99
s4 The proposed scheme is proved to be accurate and efficient. result 0.75 0.86 0.85 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.74.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular meshes. The velocity distribution function and its trace are approximated in the piecewise polynomial space of degree up to 4. The fast spectral method (FSM) is incorporated into the DG discretization to evaluate the collision operator. Specific polynomial approximation is proposed for the collision term to reduce the computational cost. The proposed scheme is proved to be accurate and efficient.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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