BEmBDF scheme for curvature driven moving stokes flows
Abstract
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 velocity field of the fluid domain is obtained by writing the governing Stokes equations in terms of an integral formulation that is solved by a Boundary Element Method (BEM). The motion of the boundary is modeled by considering the boundary curve as material points. The trajectories of those points are followed by applying the Lagrangian representation for the velocity. Substituting this representation into the discretized version of the integral equation yields a system of non linear Ordinary Differential Equations (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 BDFscheme is applied to solve those equations. Some important features with respect to the numerical implementation of this method are highlighted, like the approximation of the Jacobian matrix and the continuation of integration after a mesh redistribution. The usefulness of the method for both twodimensional and axisymmetric problems is demonstrated.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 May 1994
 Bibcode:
 1994STIN...9523144V
 Keywords:

 Backward Differencing;
 Boundary Element Method;
 Curvature;
 Deformation;
 Incompressible Flow;
 Newtonian Fluids;
 Stokes Flow;
 Viscous Fluids;
 Differential Equations;
 Fluid Boundaries;
 Lagrangian Function;
 Numerical Integration;
 Problem Solving;
 Trajectories;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer