Estudo numérico do modelo de Giesekus em escoamento bidimensional com obstáculo

Abstract

This study develops and analyzes a numerical method for simulating two-dimensional viscoelastic flows described by the Giesekus constitutive model, with emphasis on the flow around a circular cylinder confined between parallel plates. The mathematical formulation is based on the Navier-Stokes equations for incompressible fluids, written in the vorticity-velocity form, and for the implementation of the immersed obstacle, the Immersed Boundary Method is adopted, allowing the use of fixed Cartesian meshes without the need to generate meshes adjusted to the boundary.

The spatial discretization is performed using high-order compact schemes, and the temporal integration is done using the fourth-order Runge-Kutta method. For the numerical stabilization of viscoelastic regimes, the log-conformation technique is used for the evolution of the polymer stress tensor, which is especially necessary in regimes associated with high Weissenberg numbers. The solution of Poisson's equations is obtained using a multigrid method, ensuring computational efficiency.

Initially, the numerical methodology is verified by simulating classical Newtonian flows, comparing the drag coefficients and the wake structure to results available in the literature. Next, the viscoelastic flow between parallel plates is analyzed, investigating the influence of the constitutive parameters of the Giesekus model. Lastly, we move the study to the viscoelastic flow around a confined circular cylinder, evaluating the impact of fluid elasticity on the problem.

The results indicate that the drag coefficient in viscoelastic flow past a confined cylinder strongly depends on the model parameters. For a fixed Reynolds number, the drag coefficient increases with the viscosity ratio beta, while it decreases as Re increases, preserving a trend similar to the Newtonian regime. In addition, increasing the mobility parameter alpha_G is associated with a reduction in the drag coefficient, with a more pronounced effect for lower values of this parameter.