Formulation of the method of fundamental solutions for two-phase Stokes flow

Rek, Zlatko (author), Šarler, Božidar (author)

The method of fundamental solutions with a subdomain technique is used for the solution of the free boundary problem associated with a two-phase Stokes flow in a 2D geometry. The solution procedure is based on the collocation of the boundary conditions with the Stokeslets. It is formulated for the flow of unmixing fluids in contact, where the velocity, pressure field, and position of the free boundary between the fluids must be determined. The standard formulation of the method of fundamental solutions is, for the first time, upgraded for the case with mixed velocity and pressure boundary conditions and verified on a T-splitter single-phase flow with unsymmetric pressure boundary conditions. The standard control volume method is used for the reference solution. The accurate evaluation of the velocity derivatives, which are required to calculate the balance of forces at the free boundary between the fluids, is achieved in a closed form in contrast to previous numerical attempts. An algorithm for iteratively calculating the position of the free boundary that involves displacement, smoothing and repositioning of the nodes is elaborated. The procedure is verified for a concurrent flow of two fluids in a channel. The velocity and velocity derivatives show fast convergence to the analytical solution. The developed boundary meshless method is easy to code, accurate and computationally efficient since only collocation at the fixed and free boundaries is needed.

• Language: English
• Keywords: Stokes equations, two-phase flow, free boundary problems, method of fundamental solutions, subdomain technique
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: Str. 199-210
• Numbering: Vol. 158
• PID: 20.500.12556/RUL-152128-4b13f14e-f79d-5a8c-abca-c2a20e6493d6
• UDC: 532:519.62
• ISSN on article: 0955-7997
• DOI: 10.1016/j.enganabound.2023.10.024
• COBISS.SI-ID: 171090179
• Publication date in RUL: 07.11.2023

Record is a part of a journal

• Title: Engineering analysis with boundary elements
• Shortened title: Eng. anal. bound. elem.
• Publisher: Elsevier
• ISSN: 0955-7997
• COBISS.SI-ID: 5605380

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: Stokesove enačbe, dvofazni tok, problem proste meje, metoda temeljnih rešitev