Abstract
AbstractIn 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.
Highlights
Numerical simulation of single- and two-phase flows has attracted the attention of researchers in the past few decades
The modified schemes have been tested in the case of no source terms, which has shown that it produces the same results as the classical scheme
A novel extension of the Rusanov scheme has been proposed to improve the preservation of the steady-state solutions of Euler equations and the drift flux model (DFM)
Summary
Numerical simulation of single- and two-phase flows has attracted the attention of researchers in the past few decades This interest is invoked by many associated industrial applications, such as flow dynamics in petroleum refineries, distillation units, boilers of petrochemical plants and refineries, pipelines for long-distance transportation of gas and liquid[1] as well as in drilling systems.[2] Accurate prediction of the steady-state solution of such systems is crucial in the. Transient multiphase flows commonly occur in pipelines when changes in operational conditions, such as inlet and outlet flow rates, and set-point pressures, are induced. These changes are usually exerted to reach a new steady condition in the system. All these points dictate that a reliable simulator should predict transients accurately and the steady-state solution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal for Numerical Methods in Fluids
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
