We present an assessment of viscosity regularization (VR) in predicting transient flows of viscoplastic fluids (VPF). Although VR has been the most popular approach for computational studies of VPF in the last decade, the understanding of its effects on the predicted flow behaviour has remained largely qualitative. To reveal the effects of VR, we present a systematic quantitative comparison of the solutions of the regularized and exact (i.e. not regularized) problems. We consider free convection of a Bingham fluid in a two-dimensional square cavity with differentially heated sidewalls. We use bi-viscosity as a representative VR model and use augmented Lagrangian (AL) method to solve the exact problem. We show that common methods of assessing the solution error can hugely overestimate the accuracy of the results of VR. In particular, complete loss of accuracy is observed when flow conditions approach the motionless state, rendering the lower computational cost and algorithmic simplicity of VR irrelevant. Furthermore, we quantify the accuracy of bi-viscosity regularization in predicting the unyielded regions. This analysis disproves by counterexample that using yield stress contours produces convergent numerical estimates of the unyielded regions.

我们在预测粘塑性流体（VPF）的瞬态流动时提出了粘度调整（VR）的评估。尽管在过去的十年中，VR一直是VPF计算研究中最流行的方法，但是对VR对预测的流动行为的影响的理解仍然是定性的。为了揭示VR的效果，我们对正则和精确（即非正则）问题的解决方案进行了系统的定量比较。我们考虑宾汉流体在带有不同加热侧壁的二维方腔中的自由对流。我们使用双粘度作为代表VR模型，并使用增强拉格朗日（AL）方法来解决确切的问题。我们表明，评估解决方案误差的常用方法会大大高估VR结果的准确性。尤其是，当流量条件接近静止状态时，会观察到完全的精度损失，从而使VR的较低计算成本和算法简单性变得无关紧要。此外，我们在预测未屈服区域时量化了双粘度正则化的准确性。该分析通过反例证明了使用屈服应力等高线可以产生未屈服区域的收敛数值估计。