One of the greatest challenges in performing numerical simulations of viscoelastic flow is how to choose the model parameters in order to be able to achieve quantitative agreement with experimental measurements in benchmark geometries. In the present work, we revisit the original concepts of Reynolds ($Re$) and Weissenberg ($Wi$) numbers in order to provide means to adequately choose those parameters. In particular, we highlight the importance of the Oldroyd-B model as a reference for viscoelastic behavior and propose a new methodology for the comparison between general viscoelastic models and the Oldroyd-B model. We identify inconsistencies in the usual approach consensually adopted in the literature. The historical reason for that seems to have its root on the fact that Reynolds and Weissenberg numbers are recognized as expressions and not as concepts. This paradigm allows the choice of parameters of a model as characteristic quantities. We propose here to choose the Oldroyd-B model parameters for the comparison with more complex viscoelastic models so that $Re$ and $Wi$ concepts are maintained. To illustrate this matter, we simulate a flow which is known for capturing an important viscoelastic effect, the transient extrudate swell problem. We tested three viscoelastic models with intermediate levels of complexity, namely PTT, Giesekus, and FENE-P. The traditional and the proposed approaches are compared and the role of the extra parameter, that endows these models with a nonlinear character with respect to the stress, is reinterpreted. It is demonstrated that the nonlinearity introduced by this extra parameter is overestimated in the usual formulation.

进行粘弹性流动数值模拟的最大挑战之一是如何选择模型参数，以便能够与基准几何中的实验测量结果实现定量一致。在目前的工作中，我们将重温雷诺（Reynolds）的原始概念（$\mathrm{[R}Ë$）和Weissenberg（$\mathrm{w\; ^}\mathrm{一世}$），以便提供一种装置，以充分选择这些参数的数字。特别是，我们强调了Oldroyd-B模型作为粘弹性行为参考的重要性，并提出了一种用于比较一般粘弹性模型和Oldroyd-B模型的新方法。我们发现在文献中普遍采用的通常方法中存在不一致之处。造成这种情况的历史原因似乎是基于这样一个事实，即雷诺数和魏森伯格数被认为是表达而不是概念。这种范例允许选择模型的参数作为特征量。我们建议在这里选择Oldroyd-B模型参数，以便与更复杂的粘弹性模型进行比较，从而$\mathrm{[R}Ë$ 和 $\mathrm{w\; ^}\mathrm{一世}$概念得以维护。为了说明这一点，我们模拟了一个已知可以捕获重要的粘弹性效应（瞬态挤出物溶胀问题）的流。我们测试了三种中等复杂度的粘弹性模型，即PTT，Giesekus和FENE-P。比较了传统方法和建议方法，并重新解释了额外参数的作用，这些参数赋予了这些模型关于应力的非线性特征。结果表明，在通常的公式中，高估了此额外参数引入的非线性。