The method of fundamental solutions for the Stokes flow with the subdomain technique

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

The collocation version of the Method of Fundamental Solutions (MFS) with subdomains is introduced in the present work for the solution of the 2D Stokes flow in backward-facing-step geometry, including Dirichlet and Neumann boundary conditions. The motivation for the present work is the inability of the MFS to solve such problems and the problems with slits and cracks due to the discretization of a single domain. The inability stems from the artificial boundary that is difficult or impossible to properly geometrically set in such cases. The solution for such problems is found by splitting such domains into subdomains. The MFS equations for the equilibrium conditions at the collocation points on the interface between the adjacent subdomains are derived for the Stokes equation. A matrix that simultaneously solves the collocation problem on all the subdomains is formed and solved. A sensitivity study of the MFS results is performed by comparing the relative root mean square error with the reference solution obtained by the classical mesh-based finite volume method on a very fine mesh. The subdomain technique is verified by dividing the domain into 2, 3 and 5 subdomains. The velocity, vorticity and pressure compare very well with the reference solution in all three cases while the solution for the single domain approach is outstandingly poor and inappropriate. The paper shows that the proposed subdomain technique maintains the simplicity, true meshless character and accuracy of the MFS for the Stokes flow in cases where the domain topology requires the use of the subdomain technique.

• Language: English
• Keywords: method of fundamental solutions, Stokes flow, subdomain technique, interface conditions
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: Str. 80-89
• Numbering: Vol. 128
• PID: 20.500.12556/RUL-126147
• UDC: 532.51:519.876.5(045)
• ISSN on article: 0955-7997
• DOI: 10.1016/j.enganabound.2021.03.020
• COBISS.SI-ID: 59336963
• Publication date in RUL: 13.04.2021

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 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: metoda temeljnih rešitev, Stokesov tok, tehnika podobmočij, stični pogoji