A BEM/FEM Coupling Approach for Fluid-Structure Interaction Simulation of Cell Motion (Communications in Computational Physics, 2010)
In this paper, accurate and efficient simulation of cell motion in a biologicalfluid flow is investigated. The membrane of a moving cell is represented by athin shell composed of incompressible neo-Hookean elastic materials and the liquidsaround the membrane are approximated as incompressible Newtonian flows with lowReynolds numbers. The biofluid mechanics is approximated by the Stokes flow equations.A low-order BEM model is developed for the two biological fluids coupled atthe membrane surface. The moving boundary problem in fluid mechanics can be effectivelysolved using the BEM with a GMRES solver. The FEM model based on a flatthin shell element is further developed to predict the membrane load due to the largedeformation of a moving cell. Computational efficiency is greatly improved due tothe one-dimensional reduction in the present BEM and FEM models. The BEM solverfor the biological fluids is coupled with the FEM solver for the cell membrane at themembrane surface. The position of the membrane surface nodes is advanced in time byusing the classical fourth-order Runge-Kutta method. Numerical instability is avoidedby using a relatively small time step. Further numerical instabilities in the FEM solveris alleviated by using various techniques. The present method is applied to the FSIproblems of cell motion in a cylindrical flow. Numerical examples can illustrate thedistinct accuracy, efficiency and robustness of the present method. Furthermore, theimportance of bending stiffness of a cell membrane for stable cell motion simulation isemphasized. It is suggested that the present approach be an appealing alternative forsimulating the fluid-structure interaction of moving cells.