A spectral domain decomposition method for the planar non-Newtonian stick-slip problem

Abstract

A spectral domain decomposition method for solving the planar stick-slip problem for an Oldroyd-B fluid is presented. The flow domain is decomposed into two semi-infinite rectangular subdomains. A comparison of the treatment of these subdomains by domain truncation and algebraic mapping is given. A fixed point method is used to linearize the constitutive equation. The linearized systems are solved in a manner sympathetic towards the structure of the coefficient matrices at each iterative step. The algorithm employed in solving the stick-slip problem is shown to be efficient in its demand upon array storage and CPU time. The numerical results demonstrate the necessity of adequate entry and exit lengths for the non-Newtonian problem and the adverse effect that the singularity has upon the range of Weissenberg numbers over which converged solutions are possible. Results generated from a regularized stick-slip geometry where the boundary singularity is smoothed out provide evidence that it is possible to extend this range by solving a slightly modified problem in which the effect of the singularity is weakened.