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

流固耦合(FSI)问题在许多工程和应用科学领域都很重要，如血液流动的建模、结构的流致振动和波能装置等，对这类问题的数值模拟工具也引起了极大的兴趣。共轭换热(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，为也包括CHT效应的新类别的FSI问题开发稳定的分割算法。PIS将解决为这些FSI-CHT问题开发高精度格式的问题。高阶格式特别适用于高雷诺数、湍流和弹性波传播等以波动为主的区域。同时，实现分区格式的高精度界面耦合方法面临着大量的智力和数值挑战。所提出的研究涉及开发和分析一系列复杂和具有挑战性的FSI-CHT问题的新的高阶精度算法，例如涉及不可压缩或可压缩流动、可能的自由面、耦合到刚体以及具有热变形的散体的问题。这些新的分割算法将使用新的界面耦合条件来处理FSI和CHT界面条件。FSI接口条件将基于我们为附加质量分区(AMP)方案开发的原则。CHT区域耦合将扩展最近设计的CHAMP界面条件，该条件将区域分解的优化Schwarz迭代的思想与兼容性界面条件相结合。由此产生的界面耦合将提供在广泛的材料参数范围内保持稳定的方案(例如，当附加质量效应较大时，对于轻固体)。主要的重点将是不可压缩流动和不可压缩固体的算法。对于不可压缩的弹性固体和不可压缩的Navier-Stokes方程，将发展新的高精度分数步求解器。复杂的移动和变形几何体将使用变形复合网格进行处理。快速、高效、可伸缩的多重网格算法和自动网格生成算法将被开发为FSI-CHT解算器的关键组件。新的高阶准确和稳定的AMP算法将补充PI和合作者已经为FSI问题开发的算法，它们将共同提供一套开放源代码软件中随时可用的解算器。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.