For information about selecting the interpolation for pressure and velocity, see Controlling the Interpolation.
Differential viscoelastic flows explicitly introduce viscoelastic extra-stress variables or state variables in addition to velocity and pressure variables. This family of mixed representations is described as the mixed-mixed element, because the velocities act as constraints on the extra-stress tensor, and the mass conservation equation is a constraint on the velocity field.
Several interpolation schemes are available in Ansys Polyflow. For the viscoelastic tensors (extra-stress, configuration, orientation), (bi)quadratic, 2x2, 4x4 bilinear, EVSS, and DEVSS interpolations are available depending on the selected model and geometry.
In EVSS interpolation, the constitutive equation is not solved in terms of
(viscoelastic extra-stress tensor). Instead, 
is split into purely viscous and an elastic components. This
split form is substituted into the constitutive equation, which is rewritten in
terms of the elastic component and solved. Combining both viscous and elastic
components recovers the actual viscoelastic stress tensor. Further details on
the EVSS method can be found in [27] and [37].
The use of the (bi)linear interpolation for the elastic component of the stress and rate-of-deformation tensors makes the EVSS method one of the cheapest from the computational point of view. The EVSS formulation is not applicable to FENE-P, DCPP, and Leonov viscoelastic models. The DEVSS method is an alternative for these models.
The DEVSS method consists of adding a purely viscous term into the momentum equation that is expressed in terms of velocity unknowns, and removing an equivalent contribution expressed in terms of rate-of-deformation unknowns. Such a formulation keeps the constitutive equation unchanged. Further details can be found in [17]. The DEVSS method, like EVSS, uses the (bi)linear interpolation for the stress and rate-of-deformation tensors making it one of the cheapest from the computational point of view. A numerical viscosity factor has to be specified for the DEVSS method, which can be accessed through the advanced features in the menu.
By default, Ansys Polyflow considers the sum of all individual viscosity factors from all the modes. The value is automatically updated when data of the rheological model is altered. You can also specify a preferred value, which will not be updated, unless explicitly stated. In addition, the selection of a particular interpolation for the viscoelastic extra stress can be combined with a streamline-upwinding (SU) or a Galerkin technique. Streamline upwinding Petriv-Galerkin is also available, in combination with the 4x4 bilinear sub-interpolation for the viscoelastic stress.
The default upwinding schemes have been chosen for optimal stability and changing them is not recommended unless you want to experiment with a particular numerical scheme. For 2D viscoelastic flows with a single mode, you can use the so-called 4×4-SU interpolation, which combines a high discretization level for the extra-stress tensor and the streamline upwinding method. This combination is robust for solving problems where elasticity plays a significant role, especially in the presence of flow singularities, such as reentrant corners or die-exit lips. However, this method is computationally expensive.
Especially for 3D flows, viscoelastic flows calculations are often computationally expensive. This originates from the number of viscoelastic unknowns that are introduced with each of the modes. A fact is that shear stress and normal stress are the only nonvanishing components of the viscoelastic stress tensor in a simple shear flow; frequently, these stress contributions dominate in a general flow situation, while the contributions in the transverse direction are considered negligible. It is therefore reasonable to use an approximate integration of the viscoelastic constitutive equations, which tracks unknown tensors in the streamwise direction. This optional technique is referred to as the streamwise approximation for tensors (SAFT). The SAFT technique is applied to tensors invoked in viscoelastic flow simulations, and reduces the number of viscoelastic unknowns by a factor of two. Note that in order to achieve this reduction, some quantities are discarded and retrieved on the basis of an algebraic equation instead of the original differential equation.
Because the SAFT technique assumes that the transverse components of the stress tensor are negligible, it is not suitable for fluid models characterized by a nonvanishing second normal stress or normal stress difference. Hence, the SAFT technique is only made available for certain constitutive equations—namely, Maxwell, Oldroyd, and White-Metzner, as well as Phan Thien-Tanner when the second normal stress difference vanishes—and is not available for other viscoelastic models. As long as the individual contributions obey the previously listed constitutive equations, the SAFT technique can be applied to single-mode as well as multi-mode models. In addition to the constitutive equation limitations, the SAFT technique is not available for flow induced crystallization modeling (see Flow Induced Crystallization (FIC)), nor for the Narayanaswamy model used in the prediction of residual stresses and deformations (see Residual Stresses and Deformations).
The objective of the SAFT technique is to reduce the calculation time. It can be used only with the EVSS and DEVSS techniques, and is available only for flow simulations that are calculated using a 3D mesh (that is, it is not available for problems that are 2D axisymmetric, 2.5D planar and axisymmetric, and so on). Note that the SAFT approximation performs better in combination with the DEVSS technique. Also, the DEVSS technique involves a numerical viscosity factor, which can possibly be adjusted in order to compensate for the discarded stress components.
By discarding the transverse components of the stress tensor, the SAFT technique affects the balance of force; this in turn can affect some predictions. Investigations that evaluated the effect of the SAFT technique on predicted results have found that the most visible consequence is the possibility of increased extrudate swelling. Hence, it is a good practice to evaluate the consequences of the SAFT technique for a given rheological model under specific geometric and kinematic conditions. Increasing the numerical viscosity invoked by the DEVSS technique leads to an artificial increase of the corresponding transverse contribution, which can control such swelling. This originates from the fact that the SAFT technique applies only to explicitly calculated tensorial quantities.
In most cases of differential viscoelastic flows, the default scheme for
is the EVSS formulation combined with an SU
technique ([27] and [37]). In Ansys Polydata, this option corresponds to the menu item,
EVSS SU for stresses under the
Interpolation menu. The EVSS element
explicitly introduces an interpolation for the rate-of-deformation
tensor (common to all modes), and an interpolation for each
component of the viscoelastic extra-stress tensor. This allows Ansys Polyflow to use a lower interpolation order for the stress field. The EVSS element is therefore computationally less expensive than the 4x4 element, especially for the multiple-mode case. However, as mentioned previously, the EVSS technique is not available for FENE-P, DCPP, and Leonov models, and the quadratic and DEVSS-SU interpolations are selected by default for 2D and 3D flows, respectively. The quadratic interpolation is also available for the other models (only for 2D isothermal flow with a single relaxation time). In the Interpolation menu in Ansys Polydata, this option corresponds to the Quadratic element for stresses menu item. This element is not as stable as the 4x4 and EVSS elements, but requires less CPU time and memory than the 4x4 element.
All components of tensors involved in a viscoelastic flow simulation are calculated by default. It may be useful to invoke the SAFT technique for large cases, in order to speed up the calculation.
If you want to use the classical MIX1 algorithm (when available), select Quadratic element for stresses. No other parameters must be adjusted.
Quadratic element for stresses
If you have to use the algorithm based on the enriched interpolation for the viscoelastic stresses (when available), respectively with streamline upwinding technique and with streamline upwinding/Petrov-Galerkin algorithm, select:
4x4 SU element for stresses
4x4 SUPG element for stresses
No other parameters must be adjusted.
If you want the EVSS algorithm (when available), with and without the streamline upwinding technique, select:
EVSS for stresses
EVSS SU for stresses
No other parameters must be adjusted.
If you want the DEVSS algorithm with and without the streamline upwinding technique.
DEVSS for stresses
DEVSS SU for stresses
If you want to enable the SAFT technique, select Enable SAFT technique
Enable SAFT technique
Note that the SAFT technique is only available if the EVSS-SU or DEVSS-SU method is selected. Additionally, if the DEVSS-SU method is selected, the numerical viscosity can be modified via the advanced options (as explained in a description that follows). If another interpolation is subsequently selected, the SAFT technique is automatically disabled. You can disable the previously selected SAFT technique manually by selecting:
Disable SAFT technique
When the SAFT technique is invoked, related information may be found in the listing file. First of all, statements indicating the reduction of the number of unknowns are written. Next, some convergence messages will be duplicated for the viscoelastic fields; when such messages are produced, they concern the original full tensor as well as the one that results from the SAFT technique. In actuality, the first tensor depends on the second one.
To enter a value for the numerical viscosity factor, select Advanced options and choose either manual or automatic setting of the DEVSS numerical viscosity.
Advanced options
When you select the DEVSS or DEVSS-SU algorithm, it is strongly recommended that you keep a nonvanishing value for the numerical viscosity factor. The matrix of the system can become singular when a vanishing viscosity factor is used, as a result of the linear interpolation of the variable connected to the constitutive equation.
Also, when invoking the SAFT technique, the viscosity factor can be adjusted (for example, on the basis of a known result), in order to compensate for excessive swelling. Some simulation results have been shown to better match reference solutions when the numerical viscosity factor is about four times the sum of partial viscosities. This statement is empirical, and it is quite possible that a lower or a larger value may be needed under some circumstances.
For elastic problems, you can represent the displacement field as a quadratic expression, where you can avoid shear-locking when the deformation is predominately bending. The quadratic expression may be more computationally expensive, however, the results are of a higher quality.
Quadratic displacement
In some situations, the use of a robust finite-element interpolation (that is, involving many stress variables, at greater CPU expense) is required only in a small part of the computational domain. In such cases, you can select different interpolation types on different subdomains, using the Sub-interpolation menu item at the bottom of the Interpolation menu. For viscoelastic flows, this item is available only for interpolating the viscoelastic extra stresses of 2D isothermal viscoelastic flows with a single relaxation time.
For accessing the sub-interpolation menu for the extra-stress of a 2D isothermal viscoelastic flow, first select the 4x4 interpolation (SU or SUPG) for the extra-stress tensor, as explained above, then select
Sub-interpolation
and then identify the domain where a different interpolation is required.
Important: Sub-interpolating can lead to some reduction in CPU time and memory, while retaining the advantages of robustness. However, recent (and continuing) improvements in computer speed make sub-interpolation schemes less attractive.
When you specify a power-law function for viscosity and/or relaxation time in conjunction with the White-Metzner model, Ansys Polyflow will, by default, use Newton-Raphson iterations. In some cases, it may be better to use Picard iterations. See Viscosity-Related Iterations for details.
The interpolation schemes available for nonisothermal differential viscoelastic flow calculations are the same as those available for nonisothermal generalized Newtonian flow calculations. See Interpolation for Nonisothermal Flows for details.
When defining a differential viscoelastic flow, several tensorial quantities are calculated, and those depend on the selected model as well as on the selected interpolation. Although the calculated quantities are often intrinsic to the selected model, some have little interest. However, quantities such as the total extra-stress tensor have an obvious interest for the engineer.
The many calculated fields that appear in the field management menu may have names that look similar, and it can be useful to provide guidelines for discriminating among those fields. It is relatively easy to locate tensorial quantities that are created during the setup: they often contain the string of characters "STRESSES" or "DEVSS" or "EVSS". Quantities that are named "STRESSES", "T EVSS" as well as "T DEVSS" (the latter ones without any subsequent letter or integer) denote the extra-stress tensor, and are endowed with the usual meaning. The selected names sometimes suggest the integration or algorithm that was selected for the calculation.
When the names of such quantities contain a subsequent integer or letter, the corresponding field refers to some partial information (for example, in the context of multi-mode viscoelastic flow), or is endowed with another meaning. So, for example, the field "T DEVSS 1" refers to the contribution of the first mode of a multi-mode viscoelastic model solved with the DEVSS technique, while the field "STRESS A" actually denotes the configuration tensor for the FENE-P or POMPOM (DCPP) models. Although these fields can easily be inspected and interpreted for a single-mode viscoelastic model, they have usually little direct interest for you in the context of a multi-mode viscoelastic model.
The field "S EVSS" contains only a portion of the information of the stress tensor, and is therefore not appropriate for interpretation, however, the fields "D EVSS" and "D DEVSS" actually denote the rate-of-deformation tensor: these fields have the usual meaning in the sense of fluid mechanics, and can therefore always be interpreted.