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

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

The interface between two immiscible Newtonian liquids with different densities and the same viscosity, influenced by gravity, is based on the Phase-Field Method (PFM) formulation. 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 the inertial and buoyancy terms (non-Boussinesq formulation). The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in two-dimensional Cartesian coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. Implicit time discretisation is performed for the NS and CH equations in the momentum predictor and Phase-Field (PF) variable corrector steps of PISO, while the momentum corrector steps solve the NS equation explicitly. 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 author's 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.

• Language: English
• Keywords: meshless methods, simulation, numerical method, dinamika tekočin
• Work type: Article
• Typology: 1.08 - Published Scientific Conference Contribution
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 6 str.
• Numbering: Vol. 2766, art. 012163
• PID: 20.500.12556/RUL-158314
• UDC: 532:519.62
• ISSN on article: 1742-6596
• DOI: 10.1088/1742-6596/2766/1/012163
• COBISS.SI-ID: 197787651
• Publication date in RUL: 05.06.2024

Record is a part of a proceedings

• Title: Eurotherm 2024
• COBISS.SI-ID: 197654787

Record is a part of a journal

• Title: Journal of physics. Conference series
• Publisher: Institute of Physics Publishing
• ISSN: 1742-6596
• COBISS.SI-ID: 2035044

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: brezmrežne metode, simulacija, numerične metode, fluid dynamics