Title:

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

Abstract:

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.