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

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.