A moving overset grid method for interface dynamics applied to non-Newtonian Hele–Shaw flow

We present a novel moving overset grid scheme for the accurate and efficient long-time simulation of an air bubble displacing a non-Newtonian fluid in the prototypical thin film device, the Hele–Shaw cell. We use a two-dimensional generalization of Darcy’s law that accounts for shear thinning of a non-Newtonian fluid. In the limit of weak shear thinning, the pressure is found from a ladder of two linear elliptic boundary value problems, each to be solved in the whole fluid domain. A moving body fitted grid is used to resolve the flow near the interface, while most of the fluid domain is covered with a fixed Cartesian grid. Our use of body-conforming grids reduces grid anisotropy effects and allows the accurate modeling of boundary conditions.