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

该研究项目将大大改善用于模拟应用科学，工程和生物医学中重要问题的计算机算法，例如人体静脉中血流的建模，为评估外科手术和设计医疗设备和植入物提供关键数据。 流固耦合区由于其在工程和应用科学的许多领域中的重要性，不仅包括生物医学，而且还包括结构的流动诱导振动的建模，因此该项目所解决的流体与变形固体的耦合（即（飞机、海底电缆、风力涡轮机、建筑物）、波浪能装置、降落伞和气囊、声透镜、核反应堆堆芯的热膨胀以及冲击波-结构相互作用（爆炸效应）。 高效地计算流体-结构相互作用问题的精确解是非常具有挑战性的，这是由于其复杂的物理和几何特性，而且还由于具有挑战性的数学问题。 本研究所开发的新技术将解决这两个问题。由于所谓的附加质量不稳定性，大量重要的流固耦合问题难以模拟。 研究的重点是不可压缩流与弹性或刚性结构耦合的流固耦合问题。 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度的分区算法，以克服与复杂流固耦合和强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区（AMP）方案，该方案代表了该领域的一个概念性突破，为流体-结构相互作用问题提供了一条发展精确方案的道路。 AMP格式的一个重要性质是，即使对于轻质固体，当附加质量效应显著时，它们也保持稳定。新的算法将被纳入一个灵活的计算框架，将允许有效的模拟广泛的复杂的流体-结构相互作用问题。

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.