Enhancing the robustness of the immersed interface method for flow simulation

浸入式界面法采用固定网格和相应的快速求解器，可以有效地求解各种涉及界面的偏微分方程。它通过将接口诱发的跳变条件纳入数值方案，准确地捕捉了接口的影响。本研究的主要目的是提高该方法在处理三维大尺寸多尺度流动问题中的鲁棒性。PI建议：(1)以三维流固界面的三角形网格表示推导并实现该方法的跳跃条件；(2)通过将润滑理论纳入该方法来处理流动中的固体碰撞；(3)将该方法中捕获的边界条件从刚性固体扩展到可变形固体；(4)使用域分解和主从技术对该方法进行流固相互作用和双流体流动的分布式内存并行化。PI和他的学生应用这种增强的方法来研究固体颗粒在流体中的动力学和昆虫飞行的空气动力学控制策略。本研究旨在推广一种计算方法——浸入界面法，使其能够用于计算各种有趣且重要的大尺寸、多尺度的三维流动问题。特别是，PI和他的学生将该方法应用于研究流体中固体颗粒集合的动力学以及昆虫飞行的气动控制策略。广泛的生物和物理系统涉及物体的集体动力学，例如，学校，微生物菌落，粒子悬浮和沉降。在这个领域提出的研究将有助于理解、建模和设计这样的系统。有翼昆虫是自然界完美的小型飞行器的答案。了解昆虫的空气动力学对设计扑翼微型飞行器具有重要意义，该飞行器可用于军事监视、生物战探测和密闭空间侦察。PI计划在他的网页上发布一个用户友好的软件和浸入式界面方法的相关教程，以使想要使用该方法进行研究的本科生和研究生受益。这项研究的其他教育影响包括支持一个代表性不足的研究生和本科生参与计算研究。

The immersed interface method employs fixed grids and associated fast solvers to efficiently solve a variety of PDEs involving interfaces. It accurately captures the effects of interfaces by incorporating interface-induced jump conditions into numerical schemes. The main objective of this research is to enhance the robustness of this method to tackle 3-D large-size multi-scale flow problems. The PI proposes: (1) to derive and implement jump conditions for the method with a triangular mesh representation of a 3-D fluid-solid interface, (2) to handle solid collisions in a flow by incorporating into the method the lubrication theory, (3) to extend boundary condition capturing in the method from rigid solids to deformable solids, and (4) to use the domain decomposition and master-slave techniques for distributed-memory parallelization of the method for fluid-solid interaction and two-fluid flows. The PI and his students apply the enhanced method to investigate the dynamics of a collection of solid particles falling in a fluid and the aerodynamic control strategies in insect flight.The proposed research is to push a computational method, the immersed interface method, so that it can be used to compute various interesting and important 3-D flow problems that are of large sizes and multiple scales. In particular, the PI and his students apply the method to study the dynamics of a collection of solid particles falling in a fluid and the aerodynamic control strategies in insect flight. A wide range of biological and physical systems involve the collective dynamics of objects, for example, schooling, microorganism colony, and particle suspension and sedimentation. The proposed study in this area will help understand, model, and design such systems. Winged insects are nature's answer to perfect small-scale flying machines. Understanding insect aerodynamics is of great interest to engineers in designing flapping-wing micro air vehicles, which can be employed in military surveillance, biological warfare detection, and reconnaissance in confined spaces. The PI plans to disseminate on his web page a user-friendly software and the associated tutorials on the immersed interface method to benefit undergraduate and graduate students who want to use the method for their research. Other educational impact of this research includes the support of an under-represented graduate student and the involvement of undergraduate students in computational research.