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.
Keywords: Systems of conservation laws, gas flow, valve, Riemann problem, coupling conditions, chattering, maximization, control, isentropic Euler equations, $$-system
@article{M2AN_2022__56_5_1715_0,
author = {Corli, Andrea and Razafison, Ulrich and Rosini, Massimiliano D.},
title = {Coherence and flow-maximization of a one-way valve},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1715--1739},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {5},
doi = {10.1051/m2an/2022053},
mrnumber = {4454160},
zbl = {1498.35357},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022053/}
}
TY - JOUR AU - Corli, Andrea AU - Razafison, Ulrich AU - Rosini, Massimiliano D. TI - Coherence and flow-maximization of a one-way valve JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 1715 EP - 1739 VL - 56 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022053/ DO - 10.1051/m2an/2022053 LA - en ID - M2AN_2022__56_5_1715_0 ER -
%0 Journal Article %A Corli, Andrea %A Razafison, Ulrich %A Rosini, Massimiliano D. %T Coherence and flow-maximization of a one-way valve %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 1715-1739 %V 56 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022053/ %R 10.1051/m2an/2022053 %G en %F M2AN_2022__56_5_1715_0
Corli, Andrea; Razafison, Ulrich; Rosini, Massimiliano D. Coherence and flow-maximization of a one-way valve. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 5, pp. 1715-1739. doi: 10.1051/m2an/2022053
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