An Immersed Interface Method for the Simulation of Inextensible Interfaces in Viscous Fluids (Communications in Computational Physics, 2012)
In this paper, an immersed interface method is presented to simulate thedynamics of inextensible interfaces in an incompressible flow. The tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility,and the resulting augmented system is solved by the GMRES method. In this work,the arclength of the interface is locally and globally conserved as the enclosed regionundergoes deformation. The forces at the interface are calculated from the configuration of the interface and the computed augmented variable, and then applied to thefluid through the related jump conditions. The governing equations are discretized ona MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type method. The proposedmethod is applied to several examples including the deformation of a liquid capsulewith inextensible interfaces in a shear flow. Numerical results reveal that both the areaenclosed by interface and arclength of interface are conserved well simultaneously.These provide further evidence on the capability of the present method to simulateincompressible flows involving inextensible interfaces.