Phase-field formulated meshless simulation of axisymmetric Rayleigh-Taylor instability problem

Rana, Khush Bakhat (author), Mavrič, Boštjan (author), Zahoor, Rizwan (author), Šarler, Božidar (author)

A formulation of the immiscible Newtonian two-liquid system with different densities and influenced by gravity is based on the Phase-Field Method (PFM) approach. The solution of the related governing coupled Navier-Stokes (NS) and Cahn-Hillard (CH) equations is structured by the meshless Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO). The variable density is involved in all the terms. The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in Cartesian and axisymmetric coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. This solution procedure has improved stability compared to Chorin's pressure-velocity coupling, previously used in meshless solutions of related problems. The Rayleigh-Taylor instability problem simulations are performed for an Atwood number of 0.76. The DAM parameters (shape parameter of the Gaussian weight function and number of nodes in a local subdomain) are the same as in the authors’ previous studies on single-phase flows. The simulations did not need any upwinding in the range of the simulations. The results compare well with the mesh-based finite volume method studies performed with the open-source code Gerris, Open-source Field Operation and Manipulation (OpenFOAM®) code and previously existing results.

• Language: English
• Keywords: two-phase flow, phase-field, two-dimensionality, axisymmetry, diffuse approximate method, PISO
• 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: 14 str.
• Numbering: Vol. 169, pt. A, art. 105953
• PID: 20.500.12556/RUL-161962
• UDC: 532:544.27:004.94
• ISSN on article: 0955-7997
• DOI: 10.1016/j.enganabound.2024.105953
• COBISS.SI-ID: 207754243
• Publication date in RUL: 17.09.2024

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 4.0, Creative Commons Attribution-NonCommercial 4.0 International
• Link: http://creativecommons.org/licenses/by-nc/4.0/
• Description: A creative commons license that bans commercial use, but the users don’t have to license their derivative works on the same terms.

Secondary language

• Language: Slovenian
• Keywords: dvofazni tok, metoda faznega polja, dvodimenzionalnost, osnosimetričnost, brezmrežne metode