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In the present paper, the meshless localized radial basis function (RBF) is proposed for simulating of two-phase incompressible viscous flow. Due to the velocity of the shear flow is very low, the fluid can modeled by Stokes equations. For more convenience the primitive variables, i.e., pressure and velocity components of the Stokes equations are transformed into stream function formulation. The interface of the fluid system is modeled by using Cahn-Hilliard equation. The spatial terms of the governing equations are discretized numerically by using the RBF method. The temporal term is integrated by using fully implicit Euler method. The nonlinear terms of Cahn-Hilliard equation is linearized using the Picard iteration. The proposed method is applied to simulate coalescence and break-up of drops in shear flow. The numerical results show that the deformation of the interface can be modeled without any difficulties.

Numerical simulation of coalescence and break-up of drops in shear flow based on the meshless localized radial basis function method