High-Order Accurate Partitioned Algorithms for Fluid-Structure Interactions and Conjugate-Heat Transfer

流体-结构相互作用（FSI）问题在工程和应用科学的许多领域都很重要，例如血液流动的建模、结构的流动引起的振动和波能装置等，并且对这些问题的数值模拟工具有很大的兴趣。共轭传热（CHT）在许多FSI模拟中也起着重要作用，例如涡轮叶片，热交换器，核反应堆，半导体器件等的冷却。在这个项目中，pi的目标是在他们最近的成就的基础上，为包括CHT效应的新型FSI问题开发稳定的分区算法。pi将解决这些FSI-CHT问题的高阶精确方案的开发。高阶格式对于高雷诺数湍流和弹性波的传播等以波为主导的情况特别有用。同时，实现高阶精确的界面耦合方法对分割方案提出了许多智力和数值挑战。提出的研究涉及开发和分析新的高阶精确算法，用于广泛的复杂和具有挑战性的FSI-CHT问题，例如涉及不可压缩或可压缩流动的问题，可能有自由表面，耦合到刚体和具有传热的变形散装固体。这些新的分区算法将使用新的界面耦合条件来处理FSI和CHT界面条件。FSI界面条件将基于我们为我们的附加质量分区（AMP）方案开发的原则。CHT域耦合将扩展最近设计的CHAMP接口条件，该条件结合了优化的Schwarz迭代用于域分解的思想和兼容性接口条件。由此产生的界面耦合将提供在广泛的材料参数范围内（例如，当附加质量效应很大时，对于轻固体）保持可证明的稳定性的方案。主要的焦点将放在不可压缩流和不可压缩固体的算法上。对于不可压缩的弹性固体和不可压缩的Navier-Stokes方程，将开发新的高阶精确分步求解器。复杂的移动和变形几何将处理变形复合网格。快速、高效和可扩展的多网格算法和自动网格生成算法将被开发为FSI-CHT求解器的关键组件。新的高阶精确和稳定的AMP算法将补充pi和合作者已经开发的用于FSI问题的算法，并且它们将一起提供一套易于在开源软件中使用的求解器。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Fluid-structure interaction (FSI) problems are important in many areas of engineering and applied science, such as modeling of blood flow, flow-induced vibrations of structures, and wave energy devices, among others, and there is significant interest in numerical simulation tools for such problems. Conjugate heat transfer (CHT) also plays an important role in many FSI simulations, such as the cooling of turbine blades, heat exchangers, nuclear reactors, semiconductor devices, and more. In this project the PIs aim to build upon their recent achievements to develop stable partitioned algorithms for new classes of FSI problems that also include CHT effects. The PIs will address the development of high-order accurate schemes for these FSI-CHT problems. High-order schemes are especially useful for wave-dominated regimes such as high-Reynolds number turbulent flows and propagation of elastic waves. At the same time, achieving high-order accurate interface coupling approaches for partitioned schemes presents numerous intellectual and numerical challenges.The proposed research is concerned with the development and analysis of new high-order accurate algorithms for a wide range of complex and challenging FSI-CHT problems, such as those involving incompressible or compressible flows, with possible free surfaces, coupled to rigid bodies and deforming bulk solids with heat transfer. These new partitioned algorithms will use novel interface coupling conditions to treat both the FSI and CHT interface conditions. The FSI interface conditions will be based on principles we have developed for our Added-Mass Partitioned (AMP)schemes. The CHT domain coupling will extend the recently devised CHAMP interface conditions that combine ideas from optimized Schwarz iterations for domain-decomposition with compatibility interface conditions. The resulting interface couplings will provide schemes that remain provably stable for a wide range of material parameters (e.g. for light solids when added-mass effects are large). A primary focus will be on algorithms for incompressible flows and incompressible solids. New high-order accurate fractional-step solvers will be developed for both incompressible elastic solids and the incompressible Navier-Stokes equations. Complex moving and deforming geometry will be handled with deforming composite grids. Fast, efficient and scalable multigrid algorithms and automatic mesh generation algorithms will be developed as key components of the FSI-CHT solvers. The new high-order accurate and stable AMP algorithms will complement the ones already developed by the PIs and collaborators for FSI problems, and together they will provide a suite of solvers readily available in open-source software.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.