On the Numerical Implementation of Nonlinear Viscoelastic Models in a Finite-Volume Method

Numerical aspects of the implementation of nonlinear viscoelastic fluid models in a finite volume method are investigated: (1) decomposition of the discretized stress equations in such a way that diagonal dominance is maximized, in order to promote numerical stability with iterative solvers; (2) imposition of boundary conditions for the stress components normal to a wall plane, and for pressure. These issues are investigated in relation to the Giesekus constitutive equation and illustrative flow examples showing the benefits of the proposed methodology are given.