Phase-field-based simulation of axisymmetric binary fluids by using vorticity-streamfunction formulation Online publication date: Tue, 03-Nov-2015
by Jun-Jie Huang; Haibo Huang; Shi-Long Wang
Progress in Computational Fluid Dynamics, An International Journal (PCFD), Vol. 15, No. 6, 2015
Abstract: 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.
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