A meshless level-set scheme for interfacial flows

Abstract

This paper reports a novel meshless scheme for the numerical simulation of bubbles moving in an incompressible viscous fluid. In this paper, the motion of the bubble is modelled on the basis of the level set formulation for capturing the moving interface between the bubbles and the surrounding fluid, and the Navier-Stokes equations (with surface tension taken into account) for the ambient incompressible viscous flow. The new numerical scheme is then devised in which the Integrated Radial Basis Function Network (IRBFN) method is used for spatial discretization of the governing equations and high-order time stepping methods are used for temporal discretization. As a result, the moving interface is captured at all time as the zero contour of a smooth function (known as the level set function) without any explicit computation of the actual front location. A numerical simulation of two bubbles moving, stretching and merging in an incompressible viscous fluid is performed to demonstrate the working of the present scheme.