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Long time stability of a classical efficient scheme for an incompressible two-phase flow model

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T. Tachim Medjo, F. Tone

Numerical Analysis · Submitted 25 Oct 2013

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

The authors' main claim In this article we consider the implicit Euler scheme for a homogeneous two-phase flow model in a two-dimensional domain and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.

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arXiv ID1310.6993 (version 1)
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CitationF. Tone, T. Tachim Medjo. "Long time stability of a classical efficient scheme for an incompressible two-phase flow model." arXiv:1310.6993 (2013). https://pith.science/paper/RNY5TAEU
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In this article we consider the implicit Euler scheme for a homogeneous two-phase flow model in a two-dimensional domain and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this article we consider the implicit Euler scheme for a homogeneous two-phase flow model in a two-dimensional domain and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero. contribution 0.52 0.94 0.92 asserted 1.00

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Original abstract

In this article we consider the implicit Euler scheme for a homogeneous two-phase flow model in a two-dimensional domain and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.

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