On a Vlasov equation model for two-phase fluid flow

We consider the problem of water–air two-phase flow, which occurs during water aeration by air injection. We present and analyze a new model incorporating a nonlocal boundary condition, integrating the effect of the air phase through a source term applied to the water phase. This term is described u...

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Bibliographic Details
Published in:	Boundary value problems Vol. 2024; no. 1; pp. 122 - 15
Main Author:	Abdelwahed, Mohamed
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 30-09-2024 Hindawi Limited SpringerOpen
Subjects:	Aeration Air injection Analysis Approximations and Expansions Boundary conditions Boundary value problems Bubbles Difference and Functional Equations Eutrophication Fluid flow Local and NonLocal Boundary value Problems Mathematics Mathematics and Statistics Navier–Stokes equations Nonlocal boundary condition Ordinary Differential Equations Partial Differential Equations Particular method Two phase flow Vlasov equation Vlasov equations Water quality Navier–Stokes equations Two-phase flow Nonlocal boundary condition 76D05 Vlasov equation 35Q30 35Q83 Particular method
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Summary:	We consider the problem of water–air two-phase flow, which occurs during water aeration by air injection. We present and analyze a new model incorporating a nonlocal boundary condition, integrating the effect of the air phase through a source term applied to the water phase. This term is described using a kinetic approach based on the Vlasov equation. A numerical study is conducted, and numerical experiments are presented to demonstrate the effectiveness of the presented model
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-024-01932-5