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On a class of two-dimensional incomplete Riemann solvers

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José M. Gallardo, Kleiton A. Schneider, Manuel J. Castro

Numerical Analysis · Submitted 13 Nov 2018

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

The authors' main claim We propose a general class of genuinely two-dimensional incomplete Riemann solvers for systems of conservation laws.

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arXiv ID1811.05188 (version 1)
Pith IDM462VH6H, Pith's permanent record of this paper and its review
CitationJos\'e M. Gallardo, Kleiton A. Schneider, Manuel J. Castro. "On a class of two-dimensional incomplete Riemann solvers." arXiv:1811.05188 (2018). https://pith.science/paper/M462VH6H
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,598 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.76 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.22 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We propose a general class of genuinely two-dimensional incomplete Riemann solvers for systems of conservation laws. In particular, extensions of Balsara's multidimensional HLL scheme [J. Comput. Phys. 231 (2012) 7476-7503] to two-dimensional PVM/RVM (Polynomial/Rational Viscosity Matrix) finite volume methods are considered. The numerical flux is constructed by assembling, at each edge of the computational mesh, a one-dimensional PVM/RVM flux with two purely two-dimensional PVM/RVM fluxes at vertices, which take into account transversal features of the flow. The proposed methods are applicable to general hyperbolic systems, although in this paper we focus on applications to magnetohydrodynamics. In particular, we propose an efficient technique for divergence cleaning of the magnetic field that provides good results when combined with our two-dimensional solvers. Several numerical tests including genuinely two-dimensional effects are presented to test the performances of the proposed schemes.

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 We propose a general class of genuinely two-dimensional incomplete Riemann solvers for systems of conservation laws. contribution 1.00 0.92 0.36 asserted 0.99
s1 In particular, extensions of Balsara's multidimensional HLL scheme [J. Comput. contribution 0.70 0.27 0.03 asserted 0.52
s2 Phys. 231 (2012) 7476-7503] to two-dimensional PVM/RVM (Polynomial/Rational Viscosity Matrix) finite volume methods are considered. contribution 0.64 0.32 0.04 asserted 0.93
s3 The numerical flux is constructed by assembling, at each edge of the computational mesh, a one-dimensional PVM/RVM flux with two purely two-dimensional PVM/RVM fluxes at vertices, which take into account transversal features of the flow. method 0.98 0.84 0.09 asserted 1.00
s4 The proposed methods are applicable to general hyperbolic systems, although in this paper we focus on applications to magnetohydrodynamics. limitation 0.85 0.44 0.08 asserted 0.95
s5 In particular, we propose an efficient technique for divergence cleaning of the magnetic field that provides good results when combined with our two-dimensional solvers. contribution 0.89 0.92 0.10 asserted 0.95
s6 Several numerical tests including genuinely two-dimensional effects are presented to test the performances of the proposed schemes. contribution 0.43 0.94 0.12 asserted 0.94

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

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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

We propose a general class of genuinely two-dimensional incomplete Riemann solvers for systems of conservation laws. In particular, extensions of Balsara's multidimensional HLL scheme [J. Comput. Phys. 231 (2012) 7476-7503] to two-dimensional PVM/RVM (Polynomial/Rational Viscosity Matrix) finite volume methods are considered. The numerical flux is constructed by assembling, at each edge of the computational mesh, a one-dimensional PVM/RVM flux with two purely two-dimensional PVM/RVM fluxes at vertices, which take into account transversal features of the flow. The proposed methods are applicable to general hyperbolic systems, although in this paper we focus on applications to magnetohydrodynamics. In particular, we propose an efficient technique for divergence cleaning of the magnetic field that provides good results when combined with our two-dimensional solvers. Several numerical tests including genuinely two-dimensional effects are presented to test the performances of the proposed schemes.

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