Deep Learning Closure of Non-Equilibrium Fluid Mechanics
Abstract
Accurate, efficient simulation of nonequilibrium fluid mechanics remains a major challenge for the vast majority of hypersonics appl,ications. Transitional-regime flows are particularly difficult to predict but are essential for virtually every high-speed flight ve,hicle and atmospheric-reentry application. Boltzmann equation solutions using direct-simulation Monte Carlo (DSMC) methods are prohi,bitively expensive at transitional Knudsen numbers and for realistic chemistry, while Navier-Stokes solutions at these conditions ar,e known to inaccurately predict shock thickness and shock-boundary layer interaction due to the breakdown of the continuum assumptio,n.To address the urgent need for accurate yet computationally tractable predictions for transitional flows, we propose to develop a,new class of reduced-order partial differential equation (PDE) models for hypersonic flows. The cornerstone will be a physics-constr,ained modeling framework that maximally leverages the known and resolvable physics, as encoded in the Navier-Stokes equations, while, augmenting the physical model to predict sub-continuum flows using novel deep learning (DL) methods. The ultimate goal is to enable, transitional-regime predictions with DSMC-like accuracy at costs comparable to those of solving the Navier-Stokes equations.The phy,sics-constrained modeling framework will predict both freestream flows and slip-velocity boundary conditions. Our approach will be d,eveloped and evaluated on a series of progressively more-difficult hypersonics configurations in the transitional regime. High-fidel,ity training and validation data will be obtained from DSMC solutions of the Boltzmann equation. We will focus on augmenting the hea,t-flux and viscous-stress terms; incorporating chemical kinetics is also possible and will be the subject of future work. Encouragin,gly, in preliminary work, our physics-constrained DL framework accurately predicts 1D shock thicknesses in the transitional regime,,for which the Navier-Stokes equations alone are qualitatively incorrect. Finally, a mathematical theory will be proven to provide ri,gorous convergence guarantees for the model. The proposed research will establish the mathematical, numerical, and computational met,hods necessary for DL-based PDE models for nonequilibrium fluid mechanics. Additionally, a scalable, graphics-processing unit (GPU)-,accelerated software package for model development and implementation into popular flow solvers will be developed and published. Our, project will lay a foundation for accurate and tractable simulation, analysis, and design of hypersonic vehicles. Approved for Publ,ic Release.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 08, 2022
- Source ID
- N000142212441
Entities
People
- Jonathan F. MacArt
Organizations
- Office of Naval Research
- United States Navy
- University of Notre Dame