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

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

Abstract

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.

Keywords

brezmrežne metode;simulacija;numerične metode;fluid dynamics;meshless methods;simulation;numerical method;dinamika tekočin;

Data

Language:	English
Year of publishing:	2024
Typology:	1.08 - Published Scientific Conference Contribution
Organization:	UL FS - Faculty of Mechanical Engineering
UDC:	532:519.62
COBISS:	197787651
ISSN:	1742-6596
Views:	405
Downloads:	59
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	brezmrežne metode;simulacija;numerične metode;fluid dynamics;
Type (COBISS):	Article
Pages:	str. 1-6
Issue:	ǂVol. ǂ2766, [article no.] 012163
Chronology:	2024
DOI:	10.1088/1742-6596/2766/1/012163
ID:	24291052