A BEM-BDF SCHEME FOR CURVATURE DRIVEN MOVING STOKES FLOWS

A backward differences formulae (BDF) scheme, is proposed to simulate the deformation of a viscous incompressible Newtonian fluid domain in time, which is driven solely by the boundary curvature. The boundary v elocity field of the fluid domain is obtained by writing the governing Stokes equations in terms of an integral formulation that is solved b y a boundary element method. The motion of the boundary is modelled by considering the boundary curve as material points. The trajectories o f those points are followed by applying the Lagrangian representation for the velocity. Substituting this representation into the discretize d version of the integral equation yields a system of non-linear ODEs. Here the numerical integration of this system of ODEs is outlined. It is shown that, depending on the geometrical shape, the system can be stiff. Hence, a BDF-scheme is applied to solve those equations. Some i mportant features with respect to the numerical implementation of this method are high-lighted, like the approximation of the Jacobian matri x and the continuation of integration after a mesh redistribution. The usefulness of the method for both two-dimensional and axisymmetric pr oblems is demonstrated. (C) 1995 Academic Press, Inc.