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The modeling and simulation of two-phase flows is still an active researcharea, mainly when surface tension is present. One way to model the differentphases is with interface capturing methods. Two well-established interfacecapturing approaches are the level-set and phase-field methods. The level-setmethod is known for its ability to compute the surface tension accurately, andphase-field models satisfy the second law of thermodynamics. This paper reviewsand compares a level-set and a phase-field approach to simulate two-phaseflows. We use a modified level-set method, called convected level-set. Thedifference to the standard level-set method is that the re-initialization stepis embedded in the convection equation, avoiding a separate step during thecalculation. We also apply a global mass conservation procedure to enforce themass balance between phases. On the other hand, the phase-field approach uses aconservative Allen-Cahn equation with a Lagrange multiplier to conserve themass. The methods are implemented in libMesh, a parallel adaptive finiteelement library, using the same finite element formulations, time-marchingschemes, solvers, and mesh adaptivity strategies. We present numericalsolutions for the two methods considering adaptive mesh refinement andcoarsening (AMR/C). Results are analyzed and discussed.

Comparing the convected level-set and the Allen-Cahn phase-field methods in AMR/C simulations of two-phase flows