A residual‐based Allen–Cahn phase field model for the mixture of incompressible fluid flows

The hydrodynamics of fluid mixtures is receiving more and more attention in many science and engineering applications. Within the techniques for dealing with front displacements and moving boundaries between different density and/or viscosity fluids, phase fields are a class of models in which a diffusive transition region is taken into account instead of a steep interface. Although these models have a physical motivation, they require the definition of extra parameters. In order to make it less parameter dependent, the classic Allen–Cahn phase field model is modified, exploring its similarities with residual‐based discontinuity‐capturing schemes, making the phase field equation dependent on its own residual. We solve the coupling between incompressible viscous fluid flow and the phase field advective–diffusive–reactive transport to simulate the main processes in interface tension and/or buoyancy driven problems. For the solution of the Navier–Stokes and transport equations, we use a stabilized finite element formulation. The implementation has been performed using the libMesh finite element library, written in C++ , which provides support for adaptive mesh refinement and coarsening. A chemical convection benchmark problem is used to validate the proposed model, and then we solve two bubble interaction problems. Copyright © 2014 John Wiley & Sons, Ltd.