Abstract

In the first part of this talk we discuss a fractional mass-conserving Allen-Cahn phase-field model that describes the mixture of two incompressible fluids. The new fractional model allows controlling the sharpness of the interface, which is typically diffusive in integer-order phase-field models. The spatial discretization is based on a Galerkin spectral method whereas the temporal discretization is based on a stabilized ADI scheme. A number of numerical examples are provided to demonstrate the accuracy of the method and the ability to control the interface thickness between two fluids. In the second part, we will discuss about theoretical development of the fractional Navier-Stokes equations.