Finite element simulation for multiphase fluids with different densities using an energy-law-preserving method

Abstract

This paper reports the results of a numerical study on the dynamics of isothermal multiphase fluids using an energy-law-preserving method. A phase-field model is taken into account. Different to previous studies, a continuous finite element technique is used to simulate the Navier-Stokes-Cahn-Hilliard coupled model. A modified discrete energy law of the numerical simulation is derived in detail. A penalty formulation is applied for continuous conditions to ensure the stability of the pressure. The coalescence of two kissing bubbles and the rising of a lighter drop are simulated as numerical examples, and the estimated orders of the velocity gradient are computed to examine the accuracy of the numerical solution. The paper shows that in the computing process the energy law is preserved for each time step and that the errors in the discrete energy law equal less than 10−8.

Keywords

• multiphase fluids
• energy-law-preserving method
• sharp interface limit
• phase-field model
• continuous finite element technique
• numerical simulation