An implicit immersed interface method for membrane with mass density in incompressible flow
by
Long Lee
University of Wyoming
Coauthors: Randy LeVeque

The method developed in this paper is motivated by Peskin's

immersed boundary (IB) method, and allows one to model

the motion of flexible membranes with nonzero mass density or other structures immersed in viscous

incompressible fluid using a fluid solver on a fixed Cartesian grid.

The method incorporates part of the elastic restoring force

and the inertia due to the mass density into

jump conditions for the pressure, avoiding discrete dipole terms that

adversely affect the accuracy near the immersed boundary.

This has been implemented for the two-dimensional

incompressible Navier-Stokes equations using a high-resolution

finite-volume method for the advective terms and a projection method to

enforce incompressibility. In the projection step, the correct jump in

pressure is imposed in the course of solving the Poisson problem.

This gives sharp resolution of the pressure across the interface and also

gives better volume conservation than the traditional IB method.

Comparisons between this method and the

IB method are presented for several test problems.

Numerical studies of the convergence and order of accuracy are included.

PDF

Date received: March 20, 2008