Phase field simulation of Rayleigh-Taylor instability with a meshless method

The purpose of this paper is a numerical study of Rayleigh-Taylor instability problem in two dimensions, based on phase-field (PF) formulation and diffuse approximate method (DAM) meshless solution procedure, enabling single-domain fixed-node approach for coping with moving boundary problems. The problem is formulated based on three physically different models that reduce to solving Cahn-Hilliard equation in addition to the Navier-Stokes equations for incompressible fluids. The governing equations are solved by using explicit time discretization. DAM is structured with second order polynomial basis, Gaussian weighting, upwinding and local domain support. The pressure-velocity coupling is performed by the fractional step method. The assessment of the method is carried out based on different node density, weighting, and the size of the local domain support. The novel approach is verified by reproducing the boundary dynamics, consistent with the previously published results. A detailed comparison with the volume of fluid finite volume approach is presented. The combination of PF and DAM provides a valuable numerical tool for solving immiscible convective hydrodynamics problems. The paper represents a pioneering attempt in solution of Rayleigh-Taylor instability problem by a meshless solution of the phase-field formulation of the problem.