A new finite element scheme using the Lagrangian framework for simulation of viscoelastic fluid flows
Using the Lagrangian formulation, the author proposes a special finite element scheme for viscoelastic fluid flows. As a viscoelastic model, the co-deformational form of Phan-Thien Tanner (PTT) constitutive equation is used. In the co-deformational system of reference an analyticall solution of the equation is possible along the particles trajectories. Because of accurate determination of the stress tensor independenly of the velocity field, the full ellipticity of momentum equation can be utilized. On the basis of the deformation history, the author determines the independent stress. Due to explicit inclusion of the full viscous term from the viscoelastic model into the momentum equation, any stess splitting is necessary. The error is expressed in the Sobolev norm. To assess the stability of the numerical scheme, a sphere sedimentation in a tube with viscoelastic fluid is studied. The robustness of the code is proven by the simulation of Weissenberg effect for PTT fluid.
scientific article; zbMATH DE number 1762736