Stabilization of Oldroyd-B Fluid Flow Simulations Based On Eigenvalues of Conformation Tensor

Abstract

From a physical point of view, the molecular strain tensor can be represented at continuous level in viscoelastic fluids by the conformation tensor. This symmetric tensor should always be positive definite, however the positive-definiteness is sometimes lost in numerical simulations of non-Newtonian viscoelastic fluids flows at larger values of the Weissenberg number. This problem known as the High Weissenberg Number Problem (HWNP) and is characterized by the breakdown of numerical solutions. In some cases the HWNP can be avoided (or at least delayed) by adding a stress diffusion term to the transport equations for viscoelastic tensors. In this work, numerical tests are presented, demonstrating the HWNP problem and its possible cure based on stabilization method employing local addition of an artificial stress diffusion term to the transport equations, in the regions of the computational domain where the positive-definiteness of the conformation tensor can be violated.