Computational Methods for the Direct Simulation of Particulate Flow of Newtonian and Non-Newtonian Incompressible Viscous Fluids

9973318本项目的主要目标是解决模拟不可压缩牛顿和非牛顿粘性流体流动的Navier-Stokes方程的数值解，并将所得方法与适当的域嵌入方法结合起来，研究颗粒不可压缩粘性流体流动的模拟，例如，不可压缩流体和固体颗粒混合流动，通常在重力和水动力的作用下。数值方法将依赖于以下基本基本成分：(1)通过算子分裂进行时间离散化，(2)通过特征或简化为二阶波状方程的方法处理平流，(3)通过有限元进行空间逼近，(4)使用分布式拉格朗日乘子/虚拟（嵌入）域方法来定位固体颗粒并强制其刚体运动。要研究的典型非牛顿流体包括Maxwell和Oldroyd b .我们在这个项目中的目标是开发有效的方法，能够实现具有数百到数千个固体颗粒的不可压缩粘性流体混合物的三维流动的数值模拟。如此大规模的模拟具有科学计算中的重大挑战的特点，成功将依赖于在强大的并行计算机上实现的先进计算方法。有了这些模拟工具，科学界将能够更好地理解发生在化学反应器和裂缝性油藏中的复杂机制。在这些研究的结果中，我们可以期待的是橡胶材料和药物的制造技术的改进，以及石油工业中使用的钻井技术的效率的提高。

9973318The main goal of this project is to address the numerical solution of the Navier-Stokes equations modeling the flow of incompressible Newtonian and non-Newtonian viscous fluids and to combine the resulting methodology with appropriate domain embedding methods to investigate the simulation of particulate incompressible viscous fluid flows, e.g., flow of mixtures of incompressible fluids and solid particles moving, typically, under the effect of gravity and hydrodynamical forces. The numerical methodology will rely on the following basic basic ingredients:(1) Time discretization by operator splitting,(2) Treatment of advection by the method of characteristics or reduction to a second order wave-like equation,(3) Space approximation by finite elements,(4) Use of a distributed Lagrange multiplier/fictitious (embedding) domain methodology to localize the solid particles and force their rigid body motion.Typical non-Newtonian fluids to be investigated include Maxwell and Oldroyd B.Our goal in this project is to develop efficient methods, able to achieve the numerical simulation of three-dimensional flow of mixtures of incompressible viscous fluids with several hundreds to thousands of solid particles. Such large scale simulations have the characteristics of a Grand Challenge in Scientific Computing and success will rely on advanced computational methods implemented on powerful parallel computers. With these simulation tools the scientific community will be able to better understand the complicated mechanisms taking place for example in chemical reactors and in fractured oil reservoirs. Among the consequences of these investigations we can expect for example improved manufacturing techniques for rubber materials and pharmaceutical drugs, and also improved efficiency for drilling techniques used in oil Industry.