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In multiphase flow phenomena, bubbles and droplets are advected, deformed,break up into smaller ones, and coalesce with each other. A primary challengeof classical computational fluid dynamics (CFD) methods for such flows is toeffectively describe a transition zone between phases across which physicalproperties vary steeply but continuously. Based on the van der Waals theory,Allen-Cahn phase field method describes the face-to-face existence of twofluids with a free-energy functional of mass density or molar concentration,without imposing topological constraints on interface as phase boundary. Inthis article, a CFD simulation methodology is described by solving theAllen-Cahn-Navier-Stokes equations using a wavelet collocation method. Thesecond order temporal accuracy is verified by simulating a moving sharpinterface. The average terminal velocity of a rising gas bubble in a liquidthat is computed by the present method has agreed with that computed by alaboratory experiment. The calculation of the surface tension force by thepresent method also shows an excellent agreement with what was obtained by anexperiment. The up-welling and down-welling disturbances in a Rayleigh-Taylorinstability are computed and compared with that from a reference numericalsimulation. These results show that the wavelet based phase-field method is anefficient CFD simulation technique for gas-liquid or liquid-liquid flows.

A wavelet based numerical simulation technique for the two-phase flow using the phase field method