A two-parameter defect-correction method for computation of steady-state viscoelastic fluid flow

The numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge. In this paper a two-parameter defect-correction method for viscoelastic fluid flow is presented and analyzed. In the defect step the Weissenberg number is artificially reduced to solve a stable nonlinear problem. The approximation is then improved in the correction step using a linearized correction iteration. Numerical experiments support the theoretical results and demonstrate the effectiveness of the method.