Coupling conditions for isothermal gas flow and applications to valves. (April 2018)

• Record Type: Journal Article
• Authors: Corli, Andrea; Figiel, Magdalena; Futa, Anna; D. Rosini, Massimiliano
• Is Part Of: Nonlinear analysis. Volume 40(2018)
• Page Start: 403
• Page End: 427
• Publication Date: 2018-04
• Subjects: Systems of conservation laws -- Gas flow -- Valve -- Riemann problem -- Coupling conditions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.09.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider an isothermal gas flowing through a straight pipe and study the effects of a two-way electronic valve on the flow. The valve is either open or closed according to the pressure gradient and is assumed to act without any time or reaction delay. We first give a notion of coupling solution for the corresponding Riemann problem; then, we highlight and investigate several important properties for the solver, such as coherence, consistence, continuity on initial data and invariant domains. In particular, the notion of coherence introduced here is new and related to commuting behaviors of valves. We provide explicit conditions on the initial data in order that each of these properties is satisfied. The modeling we propose can be easily extended to a very wide class of valves.