CRII: OAC: Dynamically Adaptive Unstructured Mesh Technologies for High-Order Multiscale Fluid Dynamics Simulations

跨越不同空间和时间尺度的流体动力学在工程中起着至关重要的作用，特别是在理解风力涡轮机和飞机的湍流空气动力学方面。了解并最终预测运动学对工业和社会具有实际意义。然而，在实际问题中使用统一的空间分辨率的所有流体尺度的数值模拟是非常棘手的，由于能量从最大的湍流涡旋级联到最小的涡旋，在那里动能耗散成热传递。例如，风力涡轮机的流体长度尺度跨越数百米到微米，这是一个包含十多个数量级的多尺度问题。自适应网格细化通过将空间域离散为可变分辨率的网格元素并动态地和战略性地放置网格点来捕获最有意义的流体动力学以获得合理的解决方案来解决这个问题。该项目通过开发一个开源的通用框架，在由混合元素类型组成的非结构化网格上动态自适应网格细化，解决了准确有效地模拟计算流体动力学问题的挑战。最近高性能计算硬件向图形处理单元的转变在计算吞吐量和能量使用方面带来了显著的进步，但需要新的算法和软件。该项目通过在动态变化的网格环境中为这些架构共同设计有效的数值方法，弥合了这一过渡中的关键差距。此外，该方案将教育纳入其使命。本项目的技术目标是建立一个基于GPU的开源计算流体动力学框架，用于模拟可压缩Navier Stokes方程，采用高阶精度间断Galerkin方法离散化，动态适应混合元素非结构化网格。该框架将紧密集成CAD几何模型，用于在适应过程中将新添加的点放置在复杂几何形状的表面上。此外，重点放在解决包含相对身体运动的应用问题上，例如叶片分辨风力涡轮机和直升机模拟，同时解决软件复杂性问题，误差估计能力不足和几何复杂性。该框架旨在提供一个更精简、更易于使用的工作流程，需要最少的人为干预，在现代大型超级计算架构上无缝运行。该奖项反映了NSF的法定使命，并通过使用基金会的智力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 dynamics spanning disparate spatial and temporal scales plays a crucial role in engineering, especially in understanding the turbulent aerodynamics of wind turbines and aircraft. Understanding and ultimately predicting kinematics is of practical significance for industry and society. However, numerical simulation of all fluid scales in practical problems using uniform spatial resolution is severely intractable due to the energy transfer from the largest turbulent eddies that cascade down to the smallest eddies, where kinetic energy dissipates into heat. For example, the fluid length scales for a wind turbine span hundreds of meters down to microns, a multi-scale problem encompassing more than ten orders of magnitude. Adaptive mesh refinement alleviates this issue by discretizing the spatial domain into mesh elements of variable resolution and dynamically and strategically placing mesh points to capture the most meaningful fluid dynamics for a reasonable solution. This project addresses the challenge of accurately and efficiently simulating computational fluid dynamics problems by developing an open-source, general-purpose framework with dynamically adaptive mesh refinement on unstructured grids composed of mixed element types. The recent shift in high-performance computing hardware towards graphics processing units has brought significant advancements in computing throughput and energy usage but necessitates new algorithms and software. This project bridges the critical gaps in this transition by co-designing efficient numerical methods for these architectures in a dynamically changing mesh environment. Furthermore, this program integrates education into its mission. Post-secondary students and early-career researchers will be exposed to and trained for developing GPU-enabled software, aiming to cultivate a diverse and globally competitive workforce.The technical objective of this project is to create a GPU-enabled open-source computational fluid dynamics framework for modeling the compressible Navier Stokes equations, discretized using the high-order accurate discontinuous Galerkin method, on dynamically adapting mixed-element unstructured meshes. The framework will tightly integrate a CAD geometry model for placing newly added points on the surface of complex geometries during the adaptation process. Further, an emphasis is placed on solving application problems containing relative body motion, such as blade-resolved wind turbine and helicopter simulations, while addressing software complexity issues, inadequate error estimation capabilities, and geometry complexity. The framework aims to provide a more streamlined and simpler-to-use workflow, requiring minimal human intervention, which runs seamlessly on modern large-scale supercomputing architectures.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.