Phase-field-based simulation of axisymmetric binary fluids by using vorticity-streamfunction formulation (Q1753806)

Summary: We propose a numerical method for the simulation of axisymmetric binary fluids based on the phase-field theory and vorticity-streamfunction formulation. Unlike most existing methods that solve the incompressible Navier-Stokes equations in the velocity-pressure form, we recast the equations into the vorticity-streamfunction form, which only need to treat one evolution equation of the vorticity for two-dimensional (2-D) or axisymmetric (pseudo 2-D) problems. Besides, this formulation enforces the continuity equation more easily. This method is verified through a series of benchmark problems under axisymmetric conditions, including the Laplace relation for a quiescent drop, coalescence of two drops, and the contact angle of a drop on a smooth wall with given wettability. Good agreements with theoretical relations or another numerical method are achieved for all these problems.