Session: Rising Stars of Mechanical Engineering Celebration & Showcase

Paper Number: 149753

149753 - Improved Simulation of Shock-Dominated Flows Using High-Order Implicit Shock Tracking 

Research Problem: Understanding and predicting hypersonic flow is crucial to design and control vehicles that operate at extremely high speeds, e.g., those used for atmospheric re-entry, responsive space access, and prompt global strike. Computational fluid dynamics (CFD) has become an in- valuable tool to gain fundamental insight into flow physics and facilitate the prediction and control of complex flows; however, hypersonic flows present unique challenges for modern CFD methods due to the strong shocks and complex flow features, e.g., shock/shock and shock/boundary layer interaction. Highly refined hexahedral grids aligned with shocks and boundary layers (BLs) and finely tuned numerical dissipation are required to obtain accurate aerothermodynamic and unstart predictions. As a result, the overall hypersonics simulation workflow, particularly mesh generation, is highly burdensome and user-intensive, and demands substantial expertise. This makes parametric flow studies and design optimization a significant challenge and severely limits the computational hypersonics (CH) workforce. Thus, there is a significant and immediate need for novel, innovative approaches to CH to address these challenges so that hypersonic flows can accurately and reliably be predicted. This is the gap this project aims to address.

Objectives: This project aims to improve the state-of-the-art in hypersonic flow simulation technology by developing and maturing a novel numerical method with high accuracy per degree of freedom (DoF) and automated grid alignment with shocks and BLs to mitigate the hyper-sensitivity of hypersonic flow predictions to the grid and numerical dissipation. I will use the method to conduct an automated parametric study of hypersonic flow over a model vehicle with deployed control surface (sliced cone-flap) at various angles of attack and flap angles, where the interaction of shocks and BLs is crucial to obtain accurate predictions.

Technical Approach: I propose a fundamental departure from traditional methods that capture shocks and BLs to one that automatically aligns the computational grid with these features using high-order methods and optimization. My group has developed such a method that simultaneously computes the flow solution and implicitly aligns the grid with shock waves and contact discontinuities by solving an optimization problem (does not explicitly generate a mesh that conforms to the shock surface). We have shown it is able to accurately resolve two- and three-dimensional high-speed, inert and reacting flows on extremely coarse meshes, even when the shock surface is complex. This project extends the approach to hypersonic flows by accounting for viscosity and developing iterative solvers to ensure efficient parallel performance.

Outcome: A successful research campaign would improve the state-of-the-art of CH by producing a numerical method that has high accuracy per DoF, has low numerical dissipation, and leads to accurate predictions on non-ideal grids (tetrahedral elements without pre-alignment to shocks and BLs). It would also produce a computational investigation into hypersonic flow over a sliced cone- flap at various angles of attack and flap angles.

Presenting Author: Matthew Zahr University of Notre Dame

Presenting Author Biography: Matthew is an assistant professor in the Department of Aerospace and Mechanical Engineering and at the University of Notre Dame, with a concurrent appointment in the Department of Applied and Computational Mathematics and Statistics. He received his PhD in Computational and Mathematical Engineering from Stanford University in 2016 and from 2016-2018 was the Luis W. Alvarez Postdoctoral Fellow in the Department of Mathematics at Lawrence Berkeley National Laboratory. He is the 2020 recipient of the AFOSR Young Investigator Award, 2022 ONR Young Investigator Award, and 2023 NSF CAREER award. His research interests include high-order methods for computational physics, PDE-constrained optimization, model reduction, and computational methods for resolving shocks and discontinuities.

Authors:

Matthew Zahr University of Notre Dame
Tianci Huang University of Notre Dame
Charles Naudet University of Notre Dame
Huijing Dong University of Notre Dame
Alexander Perez-Reyes University of Notre Dame