Huazhong Tang

An Adaptive Phase Field Method for the Mixture of Two Incompressible Fluids

We present an  adaptive moving mesh method to solve a phase
field model for the mixture of two incompressible fluids.The
projection method is implemented on a half-staggered, moving
quadrilateral mesh to keep the velocity field divergence-free, and
 the conjugate gradient or multigrid method is employed to solve
the discrete  Poisson equations. The current algorithm is
composed by two independent parts: evolution of the governing
equations and mesh-redistribution. In the first part, the
incompressible Navier-Stokes equations are solved on a fixed
half-staggered  mesh by the rotational incremental
pressure-correction scheme, and the Allen-Cahn type of phase equation
is approximated by a  conservative, second-order accurate central
difference scheme, where the Lagrangian multiplier is used to
preserve the mass-conservation of the phase field.
The second part is an iteration procedure. During the mesh
redistribution, the phase field is remapped onto the newly
resulted meshes by the high-resolution conservative interpolation,
 while the non-conservative interpolation algorithm is applied
to the velocity field. The projection technique is used to obtain
 a divergence-free velocity field at the end of this part. The
resultant numerical scheme is stable, mass conservative, highly
efficient and fast, and capable of handling variable density and
viscosity.  Several numerical experiments are presented to
demonstrate the efficiency and robustness of
 the proposed algorithm.