CAREER: Nonlinear Finite Element Manifolds for Improved Simulation of Shock-Dominated Turbulent Flows

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

Computational Fluid Dynamics (CFD) simulations are notoriously sensitive to the underlying grid for complex flows with boundary layers, shock waves, and turbulence. High-quality, highly refined, feature-aligned grids are usually required to obtain accurate predictions; these are difficult and user-intensive to construct. The principal aim of this project is to develop new simulation technology that eliminates the extreme sensitivity of modern CFD methods to the underlying grid for shock-dominated turbulent flows. The method will be useful across many scientific disciplines, including aerospace, astrophysical, biological, and environmental flows. This research effort will be complemented with an education plan that includes a hands-on fluid dynamics module for Indiana fifth graders, a summer research program for undergraduates, and an education campaign on nonlinear manifold approximations that will feature online content, conference short courses, and open-source software. This project will develop the theoretical and algorithmic foundations for using nonlinear manifolds as the basis for high-fidelity CFD simulations, an unexplored research frontier, to circumvent the limitations of existing methods with regard to complex flow phenomena. Specific nonlinear manifolds will be constructed to tailor the underlying approximation space to complex flow features on generic grids: (1) trigonometric manifolds to represent boundary layers, (2) compositional mappings to represent viscous shocks, and (3) autoencoders to represent more general features, including turbulent eddies and flow instabilities. By tailoring the underlying approximation space to the flow features instead of the grid, nonlinear approximations can dramatically improve the accuracy per degree of freedom and reduce the sensitivity of CFD predictions to the computational grid relative to conventional methods based on linear approximation spaces. As such, this project has great potential to deliver a novel and transformational CFD technology with enhanced accuracy, reliability, and automation of high-fidelity simulations of shock-dominated turbulent flows. A scalable implementation of the new approach will be disseminated in an open-source Julia solver to facilitate transition of the developments in this project to the research community. 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.