A finite-difference formulation is applied to track solid–liquid boundaries on a fixed
underlying grid. The interface is not of finite thickness but is treated as a discontinuity and is …

We present a phase-field model for the dynamics of the interface between two inmiscible
fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic …

The immersed boundary method is known to exhibit a high degree of numerical stiffness
associated with the interaction of immersed elastic fibres with the surrounding fluid. We …

An algorithm for the solution of general isotropic nonlinear wave equations is presented. The
algorithm is based on a symmetric factorization of the linear part of the wave operator …

We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity
contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in …

A Hele-Shaw cell is a device for investigating the twodimensional flow of viscous fluids in a
narrow gap between two parallel plates. Through the similarity in their governing equations …

We investigate the dynamic generation of capillary waves in two-dimensional, inviscid, and
irrotational water waves with surface tension. It is well known that short capillary waves …

In this paper, the viscous fingering phenomena of the magnetic liquids in the case when the
magnetic field is applied normally to the Hele–Shaw cell is investigated by the numerical …

A numerical procedure which is based on an integral equation for the normal velocity at the
interface is developed for the unstable flow with surface tension in a Hele-Shaw cell. The …

Abstract We study the Saffman-Taylor instability of an air bubble expanding into a non-
Newtonian fluid in a Hele-Shaw cell. We use a thin gap limit to reduce a continuum …