An Approximate Well-Balanced Upgrade of Godunov-Type Schemes for the Isothermal Euler Equations and the Drift Flux Model with Laminar Friction and Gravitation

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Samenvatting

In this article, approximate well‐balanced (WB) finite‐volume schemes are developed for the isothermal Euler equations and the drift flux model (DFM), widely used for the simulation of single‐ and two‐phase flows. The proposed schemes, which are extensions of classical schemes, effectively enforce the WB property to obtain a higher accuracy compared with classical schemes for both the isothermal Euler equations and the DFM in case of nonzero flow in the presences of both laminar friction and gravitation. The approximate WB property also holds for the case of zero flow for the isothermal Euler equations. This is achieved by defining a relevant average of the source terms which exploits the steady‐state solution of the system of equations. The new extended schemes reduce to the original classical scheme in the absence of source terms in the system of equations. The superiority of the proposed WB schemes to classical schemes, in terms of accuracy and computational effort, is illustrated by means of numerical test cases with smooth steady‐state solutions. Furthermore, the new schemes are shown numerically to be approximately first‐order accurate.
Originele taal-2Engels
Pagina's (van-tot)1110-1142
Aantal pagina's33
TijdschriftInternational Journal for Numerical Methods in Fluids
Volume93
Nummer van het tijdschrift4
Vroegere onlinedatum24 sep 2020
DOI's
StatusGepubliceerd - apr 2021

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