Numerical Simulation of Complex Incompressible Viscous Flow in Time Varying Geometries: Applications

近年来，研究人员在不可压缩粘性流动的N-S方程及其粘弹性和粘塑性二维和三维推广的模拟方面取得了新的进展，这使得这项具有挑战性的三维问题成为可能。具体地说，作者打算研究三维管道和水平钻井中压力驱动的颗粒流动的直接模拟，流体是牛顿流体或非牛顿流体，颗粒数量在数千之间。他们还将研究三叶人工心脏瓣膜周围血液流动的直接数值模拟。这些问题需要方法学上的进步，如碰撞的数值处理，粘性流体中非球形物体的运动，以及虚拟区域和Chimera类型方法的耦合，以改进边界层的处理。在过去的六年里，该奖项的研究人员开发了一种非常适合于具有移动边界的区域内流动的数值模拟的方法。由此产生的方法论已经被作者和其他科学家和工程师成功地应用于解决来自科学和工程的难题。在这些问题中，沉降、流态化和颗粒传输现象的直接模拟在科学和工程(石油工程、食品工业等)的各个领域中发挥着重要作用。该项目的主要目标是(1)改进现有的方法，以便能够处理相对复杂形状的颗粒的流体/颗粒相互作用，(2)开发现实的模型和有效的方法来计算处理流体/颗粒相互作用中发生的碰撞，(3)将所产生的方法应用于心血管医学中的一个重要问题，即血液流动/心脏瓣膜相互作用的模拟，以及(4)模拟水平管道和油井中的泥浆输送，这是提高石油采收率的一个重要问题。在心脏瓣膜项目中，目标是使用模拟工具设计人工心脏瓣膜，产生的凝血酶(一种导致动脉凝结的天然血液增稠剂)比目前使用的人工心脏瓣膜要少得多，目前使用的人工心脏瓣膜需要患者服用血液稀释剂，这些药物通常会对健康产生有害的副作用。人们希望，通过改进设计，即使不能消除，对血液稀释剂的需求也将大幅减少。该项目的这一部分将与美国和欧洲的心血管专家(包括心脏外科医生)合作完成。

Recent progress by the investigators in the simulation of incompressible viscous flow modeled by the Navier-Stokes equations and their visco-elastic and visco-plastic generalizations in two and three dimensions has led to the proposed work in challenging three-dimensional problems. Specifically, the authors intend to study the direct simulation of pressure-driven particulate flow in three dimensional pipes and horizontal drilling wells, the fluid being either Newtonian or non-Newtonian with the number of particles ranging in the thousands. They will also study the direct numerical simulation of blood flow around three-leaflet prosthetic heart valves. These problems require methodological advances such as the numerical treatment of collisions, the motion of non-spherical objects in viscous fluids and the coupling of fictitious domain and Chimera type methods in order to improve the treatment of boundary layers. During the past six years, the investigators of this award have developed a methodology well suited to numerical simulation of flow in regions with moving boundaries. The resulting methodology has been successfully applied by the authors and other scientists and engineers to the solution of difficult problems from Sciences and Engineering. Among these problems are the direct simulation of sedimentation, fluidization and particle transport phenomena, which play an important role in various areas in Sciences and Engineering (Petroleum Engineering, Food Industry,...). The main goals of this project are to (1) improve the existing methodology so that it can address fluid/particle interaction for particles of relatively complicated shape, (2) develop realistic models and efficient methods for the computational treatment of the collisions taking place in fluid/particle interactions, (3) apply the resulting methodology to an important problem in cardio-vascular medicine namely, the simulation of blood flow/heart valve interaction and (4) simulate slurry transportation in horizontal pipelines and wells, an important issue in enhanced oil recovery. In the heart valve project, the goal is to use the simulation tool to design artificial heart valves generating much less thrombin (a natural blood thickener causing artery clotting) than the ones currently used, which require the patient to take blood thinning drugs which have in general health damaging side effects. The hope is that with an improved design the need for blood thinners will be substantially reduced if not eliminated. This part of project will be done in collaboration with cardio-vascular specialists (including heart surgeons) in the USA and Europe.