In this work, a new methodology to solve the governing equations of viscoelastic fluid flows is proposed. This methodology is based on the finite-volume method with co-located arrangement of the variables, using high-order approximations for the linear and nonlinear average fluxes in the interfaces and for the nonlinear terms resulting from the discretization of the constitutive equations. In this methodology, the average values of the variable in the volumes are used during the resolution, and the point values are recovered in the post-processing step by deconvolution of the average values. The nonlinear equations, resulting from the discretization technique, are solved simultaneously, using the Newton's method. The solutions obtained are oscillation-free and accurate, as can be seen in the solution of the stick-slip flow, used as an illustrative example.
Viscoelastic fluids; simulation; finite-volume method
