| Issue |
ESAIM: M2AN
Volume 56, Number 5, September-October 2022
|
|
|---|---|---|
| Page(s) | 1715 - 1739 | |
| DOI | https://doi.org/10.1051/m2an/2022053 | |
| Published online | 20 July 2022 | |
Coherence and flow-maximization of a one-way valve
1
Department of Mathematics and Computer Science, University of Ferrara, 44121 Ferrara, Italy
2
Laboratoire de Mathématiques de Besançon, CNRS UMR 6623, Université Bourgogne Franche-Comté, 16 route de Gray, 25030 Besançon, France
3
Uniwersytet Marii Curie-Skłodowskiej, Plac Marii Curie-Skłodowskiej, 1 20-031 Lublin, Poland
* Corresponding author: ulrich.razafison@univ-fcomte.fr
Received:
16
August
2021
Accepted:
3
June
2022
We consider a mathematical model for the gas flow through a one-way valve and focus on two issues. First, we propose a way to eliminate the chattering (the fast switch on and off of the valve) by slightly modifying the design of the valve. This mathematically amounts to the construction of a coupling Riemann solver with a suitable stability property, namely, coherence. We provide a numerical comparison of the behavior of the two valves. Second, we analyze, both analytically and numerically, for several significative situations, the maximization of the flow through the modified valve according to a control parameter of the valve and time.
Mathematics Subject Classification: 35L65 / 35L67 / 76B75
Key words: Systems of conservation laws / gas flow / valve / Riemann problem / coupling conditions / chattering / maximization / control / isentropic Euler equations / p-system
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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