ON THE CAPABILITIES OF THE DOUBLE-LAYER REPRESENTATION FOR STOKES FLOWS .3. NUMERICAL APPROXIMATION

Boundary-integral equations of the second kind for Stokes flows known as the completed-double-layer (CDL) representation are promising formu lations for the solution of many-body problems in suspension mechanics . The application of polynomial interpolation and uniform versus other refinement schemes for three-dimensional triangular elements to solve the CDL representation is examined. The case of particles in close pr oximity is considered since, for this geometry, the double-layer densi ty shows significant spatial oscillations. Other pertinent topics such as numerical integrations, error estimates, and iterative schemes are addressed and numerical examples are presented. It is shown that the convergence of the numerical results (with respect to uniform refineme nt) using quadratic interpolants is fast at gaps larger than 10% of th e particle radius with uniform refinement. For gaps smaller than 10%, the interpolation should accompany a better refinement scheme. This wo rk presents an axial Chebyshev refinement scheme which is shown to be very effective in this respect.