Abstract
In this paper, we present a numerical investigation for simulating fluid-fluid interface of isothermal multi-phase fluids with a phase field model. Unlike the previous work, we use continuous finite element method to compute the governing equations and get a discrete energy law equation with a special designed scheme which is almost the same as the continuous energy law. We deal with the stability in pressure by using a penalty formulation to rewrite the continuity condition. The accuracy of calculation is examined by numerical simulation of coalescence of two kissing bubbles. And the accuracy of the discrete energy law is validated as the error in the energy law of numerical examples falls below discrete level is preserved at each time step.
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