It is possible to compute (differential) viscoelastic fluids in conjunction with the VOF model, by using a DEVSS formulation with a stabilized linear velocity/constant pressure interpolation. This section addresses the additional intrinsic difficulties that you must consider when attempting such modeling.
When a fluid model simulates a viscoelastic flow, more variables (for example, stresses) are involved. As for any viscoelastic model, this means that more CPU time and memory is required. But the model also becomes severely nonlinear (as opposed to a generalized Newtonian flow, where the degree of nonlinearity is frequently moderate), and hence runs the risk of requiring significantly more iterations and experiencing trouble converging.
Fortunately, the VOF model is shielded from the effects of nonlinearity to some degree, owing to its time-dependent approach. It is often the case that a VOF simulation has small time steps, as a result of the Courant-type limitation; as the time steps become very small, the time derivative in the constitutive equation (for example, Equation 11–5) dominates the other terms, including the nonlinear terms. This is the ideal case, however; while it holds true as you approach the limit of infinitely small time steps, in reality the other terms of the equation can still create difficulties with regard to nonlinearity and convergence. But if the time steps are reasonably small, you can expect that at the very least a linear term dominates. This is good news, as linear problems do converge. Therefore it can be said that from the point of view of the VOF model, the simulation of a viscoelastic flow does not pose major additional difficulties.
Important: Note that it is impractical to use a tool such as evolution with the VOF model (which again, inherently has small time steps) to handle the nonlinearity of a viscoelastic flow, as the computational expense of the resulting simulation would be extreme.
If you model a viscoelastic fluid as part of a VOF simulation, it is recommended that you take into account the inertia terms and introduce a nonvanishing density (this is not the default). This has the advantage of making the momentum equation evolutionary with respect to time (because in this case, time derivatives are maintained), and thus creates a link between the velocity fields at the current and previous time steps. You can expect this to facilitate most nonlinear problems in a VOF model, provided that the Reynolds number remains small (ideally lower than 1). This is a reasonable limitation, because the Reynolds number of a polymer flow is always low.