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Analytical implementation of Roe solver for two-layer shallow water equations with accurate treatment for loss of hyperbolicity

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Nino Krvavica, Miran Tuhtan, Gordan Jelenić

Computational Physics · Submitted 26 Oct 2018

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

The authors' main claim The proposed A-Roe scheme is as accurate as the Roe scheme, but much faster, with computational speeds closer to the GFORCE and IFCP scheme.

how it is stated · asserted 1.00 read the record →

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arXiv ID1810.11285 (version 2)
Pith IDISZR2HOZ, Pith's permanent record of this paper and its review
CitationGordan Jeleni\'c, Miran Tuhtan, Nino Krvavica. "Analytical implementation of Roe solver for two-layer shallow water equations with accurate treatment for loss of hyperbolicity." arXiv:1810.11285 (2018). https://pith.science/paper/ISZR2HOZ
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,525 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.72 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

A new implementation of the Roe scheme for solving two-layer shallow-water equations is presented in this paper. The proposed A-Roe scheme is based on the analytical solution to the characteristic quartic of the flux matrix, which is an efficient alternative to a numerical eigensolver. Additionally, an accurate method for maintaining the hyperbolic character of the governing system is proposed. The efficiency of the quartic closed-form solver is examined and compared to numerical eigensolvers. Furthermore, the accuracy and computational speed of the A-Roe scheme is compared to the Roe, Lax-Friedrichs, GFORCE, PVM, and IFCP schemes. Finally, numerical tests are presented to evaluate the efficiency of the iterative treatment for the hyperbolicity loss. The proposed A-Roe scheme is as accurate as the Roe scheme, but much faster, with computational speeds closer to the GFORCE and IFCP scheme.

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 A new implementation of the Roe scheme for solving two-layer shallow-water equations is presented in this paper. contribution 1.00 0.91 0.05 asserted 0.99
s1 The proposed A-Roe scheme is based on the analytical solution to the characteristic quartic of the flux matrix, which is an efficient alternative to a numerical eigensolver. method 0.82 0.86 0.08 asserted 1.00
s2 Additionally, an accurate method for maintaining the hyperbolic character of the governing system is proposed. contribution 0.93 0.89 0.06 asserted 0.99
s3 The efficiency of the quartic closed-form solver is examined and compared to numerical eigensolvers. method 0.53 0.91 0.04 asserted 0.86
s4 Furthermore, the accuracy and computational speed of the A-Roe scheme is compared to the Roe, Lax-Friedrichs, GFORCE, PVM, and IFCP schemes. method 0.71 0.90 0.08 asserted 0.93
s5 Finally, numerical tests are presented to evaluate the efficiency of the iterative treatment for the hyperbolicity loss. method 0.65 0.91 0.05 asserted 0.65
s6 The proposed A-Roe scheme is as accurate as the Roe scheme, but much faster, with computational speeds closer to the GFORCE and IFCP scheme. result 0.99 0.93 0.70 asserted 1.00

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

What was examined, and what was not

sources read
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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

A new implementation of the Roe scheme for solving two-layer shallow-water equations is presented in this paper. The proposed A-Roe scheme is based on the analytical solution to the characteristic quartic of the flux matrix, which is an efficient alternative to a numerical eigensolver. Additionally, an accurate method for maintaining the hyperbolic character of the governing system is proposed. The efficiency of the quartic closed-form solver is examined and compared to numerical eigensolvers. Furthermore, the accuracy and computational speed of the A-Roe scheme is compared to the Roe, Lax-Friedrichs, GFORCE, PVM, and IFCP schemes. Finally, numerical tests are presented to evaluate the efficiency of the iterative treatment for the hyperbolicity loss. The proposed A-Roe scheme is as accurate as the Roe scheme, but much faster, with computational speeds closer to the GFORCE and IFCP scheme.

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