Positive definiteness preserving approaches for viscoelastic flow of Oldroyd-B and FENE-CR types: Applications to particulate flow

Oldroyd-B 和 FENE-CR 类型粘弹性流的正定性保持方法：在颗粒流中的应用

• 批准号: 1418308
• 负责人: Tsorng-whay Pan
• 金额: $ 23.42万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1418308&HistoricalAwards=false
• 关键词: Positive; definiteness; preserving; approaches; viscoelastic

The motion of particles in fluids is not only of fundamental theoretical interest, but is also of importance in many applications to industrial processes involving particle-laden materials. While numerical methods for simulating particle motion in Newtonian fluids have been very successful, numerically simulating particle motion in viscoelastic fluids is quite complicated and challenging. Through the computational methodologies explored in this project, efficient simulations will be performed to investigate and understand the complex fluid-particle and particle-particle dynamics in viscoelastic fluids, especially the sedimentation, migration, lift-off and resuspension of particles in three dimensional channels. The simulation tools developed in this project will have significant engineering and biomedical applications, such as proppant transport in hydraulic fracturing operations used in oil and gas wells and the elasto-inertial particle focusing for developing cost-effective labs-on-a-chip such as cell counting devices.Numerical methods for simulating particle motion in viscoelastic fluids is quite complicated and challenging. One of the difficulties for simulating viscoelastic flows is the breakdown of the numerical methods. It has been widely believed that the lack of positive definiteness preserving property of the conformation tensor at the discrete level during the entire time integration is one of the reasons for the breakdown. To preserve the positive definiteness property of the conformation tensor, the constitutive equation can be reformulated as equations for the matrix logarithm of the conformation tensor to preserve the property of the positive definiteness as Fattal and Kupferman did. Another approach is to factorize the conformation tensor and then to write down the new associated equations at the discrete level, and hence the positive definiteness of the conformation tensor is forced as Lozinski and Owens did. In this project, we aim to extend and combine fictitious domain based distributed Lagrange multiplier methods, which is for simulating particle motion in fluid, with either the Lozinski and Owens' factorization approach or the log-conformation tensor approach via an operator splitting technique to preserve the positive definiteness property of the conformation tensor for simulating particle motion in viscoelastic fluids of Oldroyd-B and FENE-P types. Through the computational methodologies proposed in this project, efficient simulations will be performed to investigate and understand the complex fluid-particle and particle-particle dynamics in viscoelastic fluids, especially the sedimentation, migration, lift-off and resuspension of particles in two and three dimensional channels.

颗粒在流体中的运动不仅具有基本的理论意义，而且在涉及颗粒负载材料的工业过程的许多应用中也具有重要意义。虽然用于模拟牛顿流体中的颗粒运动的数值方法已经非常成功，但是数值模拟粘弹性流体中的颗粒运动是相当复杂和具有挑战性的。通过本项目中探索的计算方法，将进行有效的模拟，以研究和理解粘弹性流体中复杂的流体-颗粒和颗粒-颗粒动力学，特别是三维通道中颗粒的沉降，迁移，提离和再悬浮。该项目开发的模拟工具将具有重要的工程和生物医学应用，例如用于石油和天然气威尔斯的水力压裂操作中的支撑剂输送以及用于开发成本有效的芯片实验室（如细胞计数装置）的弹性惯性颗粒聚焦。粘弹性流动数值模拟的难点之一是数值方法的不足。人们普遍认为，构象张量在整个时间积分过程中在离散水平上缺乏正定性保持性质是崩溃的原因之一。为了保持构象张量的正定性，本构方程可以像Fattal和Kupferman那样，转化为构象张量的矩阵对数方程，以保持正定性。另一种方法是对构象张量进行因式分解，然后在离散水平上写出新的关联方程，因此构象张量的正定性被强制为Lozinski和Owens所做的。在这个项目中，我们的目标是扩展和联合收割机虚拟域为基础的分布式拉格朗日乘子方法，这是用于模拟颗粒在流体中的运动，无论是Lozinski和Owens的因式分解方法或对数构象张量的方法，通过算子分裂技术，以保持正定性质的构象张量模拟Oldrophil-B和FENE-P型粘弹性流体中的颗粒运动。通过本项目提出的计算方法，将进行有效的模拟，以研究和理解粘弹性流体中复杂的流体-颗粒和颗粒-颗粒动力学，特别是颗粒在二维和三维通道中的沉降、迁移、提离和再悬浮。