Simulation of planar converging flow of a Leonov viscoelastic fluid

Abstract An efficient finite element algorithm is presented to simulate the planar converging flow for the viscoelastic fluid of the Leonov model. The governing equation set, composed of the continuity, momentum and constitutive equations for the Leonov fluid flow, is conveniently decoupled and a two‐stage cyclic iteration technique is employed to solve the velocity and elastic strain fields separately. Artificial viscosity terms are imposed on the momentum equations to relax the elastic force and data smoothing is performed on the iterative calculations for velocities to further stabilize the numerical computations. The calculated stresses agree qualitatively with the experimental measurements and other numerically simulated results available in the literature. Computations were successful to moderately high values of Deborah number of about 27·5.