High-Order Added-Mass Partitioned Algorithms for Fluid-Structure Interaction Problems

这项研究项目将极大地改进用于模拟应用科学、工程和生物医学中的重要问题的计算机算法，例如人体静脉中的血液流动的建模，这为评估外科手术程序和设计医疗器械和植入物提供了关键数据。本项目涉及的流体-结构相互作用(即流体与变形固体的耦合)领域目前受到越来越多的关注，因为它在工程和应用科学的许多领域具有重要意义，不仅包括生物医学，而且还包括对结构(飞机、海底电缆、风力涡轮机、建筑物)、波能设备、降落伞和安全气囊、声波透镜、核反应堆堆芯中的热膨胀以及冲击波-结构相互作用(爆炸效应)的流体诱发振动的建模。由于流固耦合问题复杂的物理和几何性质，以及具有挑战性的数学问题，高效地计算流固耦合问题的精确解是非常具有挑战性的。该项目开发的新技术将解决这两个挑战。由于所谓的附加质量不稳定性，一大类重要的流固耦合(FSI)问题很难模拟。研究的重点是不可压缩流与弹性或刚性结构耦合的FSI问题。特别令人感兴趣的是流体的质量和结构的质量相似的问题，例如在血液动力学的应用中，附加质量效应很强。该项目的总体目标是为FSI问题开发稳定和高阶精确的划分算法，以克服与复杂的流固耦合和强烈的附加质量效应相关的数值困难。这些算法将基于新设计的附加质量分割(AMP)格式，它代表了该领域的概念突破，为开发流体-结构相互作用问题的精确格式提供了一条前进的道路。AMP格式的一个重要性质是，当附加质量效应显著时，即使对于轻固体，它们也保持稳定。新的算法将被整合到一个灵活的计算框架中，这将允许对广泛类别的复杂流固相互作用问题进行有效的模拟。

This research project will dramatically improve computer algorithms used for the simulation of important problems in applied science, engineering, and bio-medicine, such as the modeling of blood flow in human veins, which provides critical data to evaluate surgical procedures and to design medical devices and implants. The area of fluid-structure interaction (i.e. coupling fluids with deforming solids), which this project addresses, is of current and growing interest due to its importance in many areas of engineering and applied science, including not only bio-medicine but also the modeling of flow-induced vibrations of structures (aircraft, undersea cables, wind turbines, buildings), wave energy devices, parachutes and airbags, acoustic lenses, thermal expansion in nuclear reactor cores, and shock-structure interactions (blast effects). Computing accurate solutions of fluid-structure interaction problems efficiently is very challenging due to their complex physical and geometrical properties, but also due to challenging mathematical issues. The new techniques developed by this project will address both these challenges.A wide class of important fluid-structure interaction (FSI) problems are difficult to simulate due to the so-called added mass instability. The focus of the research is on FSI problems coupling incompressible flow with elastic or rigid structures. Of particular interest are problems in which the mass of the fluid and that of the structure are similar, such as in applications of hemodynamics, where added-mass effects are strong. The overarching goal of this project is to develop stable and high-order accurate partitioned algorithms for FSI problems that overcome the numerical difficulties associated with complex fluid-solid couplings and strong added-mass effects. These algorithms will be based on newly devised Added-Mass Partitioned (AMP) schemes that represent a conceptual breakthrough in the field by providing a path forward to develop accurate schemes for fluid-structure interaction problems. An important property of AMP schemes is that they remain stable even for light solids when added-mass effects are significant. The new algorithms will be incorporated into a flexible computational framework that will allow efficient simulations for wide class of complex fluid-structure interaction problems.