Kinetic formulation of a 2 × 2 hyperbolic system arising in gas chromatography

Christian Bourdarias; Marguerite Gisclon; Stéphane Junca

doi:10.3934/krm.2020030

Article Contents

2020, Volume 13, Issue 5: 869-888. Doi: 10.3934/krm.2020030

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Kinetic formulation of a 2 × 2 hyperbolic system arising in gas chromatography

1.
Université Savoie Mont Blanc, LAMA, UMR CNRS 5127, 73376 Le Bourget-du-Lac Cedex, France
2.
Université Côte d'Azur, LJAD, Inria & CNRS 7351, Parc Valrose, 06108 Nice

Received: May 2019

Revised: March 2020

Published: August 2020

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Abstract

A particular 2x2 hyperbolic system commonly used in the context of gas-solid chromatography is reformulated as a single kinetic equation using an additional kinetic variable. A kinetic numerical scheme is built from this new formulation and its behavior is tested on solving the Riemann problem in different configurations leading to single or composite waves.

Keywords:

Mathematics Subject Classification: Primary: 35L65, 65M08; Secondary: 35L45, 35Q79, 92E20, 76T99.

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Figure 1. Contact discontinuity. Exact and computed solutions at $ t = 1 $ along the column $ 0\leq x\leq 0.1 $

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Figure 2. Contact discontinuity: $ -\log(Erel) $ vs $ -\log(\Delta t) $

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Figure 3. Contact discontinuity: CPU time vs $ N $

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Figure 4. Solution to the Riemann Problem for $ c $

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Figure 5. Adsorption step with the BET isotherm. Exact and computed solutions at $ t = 1 $ along the column $ 0\leq x\leq 0.1 $

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Figure 6. Function $ f $ associated with the binary Langmuir isotherm

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Figure 7. Adsorption step with the binary Langmuir isotherm. Exact and computed solutions at $ t = 1 $ along the column $ 0\leq x\leq 0.1 $

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Figure 8. Desorption step (bottom) with the binary Langmuir isotherm. Exact and computed solutions at $ t = 1 $ along the column $ 0\leq x\leq 0.1 $

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Figure 9. Rarefaction: $ -\log(Erel) $ vs $ -\log(\Delta t) $

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Figure 10. Rarefaction: CPU time vs $ N $

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Figure 11. Data for the Riemann problem

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Figure 12. Shocks chords are shown as dashed lines. On the left $ c^- $ is connected to $ c^+ $ via a shock (S), a rarefaction wave (R) and a shock. On the right, $ c^- $ is connected to $ c^+ $ via a shock and a rarefaction wave

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