Antony Jameson

Kevin T. Carlberg, Antony Jameson, Mykel J. Kochenderfer et al.

Data I/O poses a significant bottleneck in large-scale CFD simulations; thus, practitioners would like to significantly reduce the number of times the solution is saved to disk, yet retain the ability to recover any field quantity (at any time instance) a posteriori. The objective of this work is therefore to accurately recover missing CFD data a posteriori at any time instance, given that the solution has been written to disk at only a relatively small number of time instances. We consider in particular high-order discretizations (e.g., discontinuous Galerkin), as such techniques are becoming increasingly popular for the simulation of highly separated flows. To satisfy this objective, this work proposes a methodology consisting of two stages: 1) dimensionality reduction and 2) dynamics learning. For dimensionality reduction, we propose a novel hierarchical approach. First, the method reduces the number of degrees of freedom within each element of the high-order discretization by applying autoencoders from deep learning. Second, the methodology applies principal component analysis to compress the global vector of encodings. This leads to a low-dimensional state, which associates with a nonlinear embedding of the original CFD data. For dynamics learning, we propose to apply regression techniques (e.g., kernel methods) to learn the discrete-time velocity characterizing the time evolution of this low-dimensional state. A numerical example on a large-scale CFD example characterized by nearly 13 million degrees of freedom illustrates the suitability of the proposed method in an industrial setting.

Philipp Birken, Jonathan Bull, Antony Jameson

We consider multigrid methods for finite volume discretizations of the Reynolds Averaged Navier-Stokes (RANS) equations for both steady and unsteady flows. We analyze the effect of different smoothers based on pseudo time iterations, such as explicit and additive Runge-Kutta (ARK) methods. Furthermore, we derive the new class of additive W (AW) methods from Rosenbrock smoothers. This gives rise to two classes of preconditioned smoothers, preconditioned ARK and additive W (AW), which are implemented the exact same way, but have different parameters and properties. The new derivation allows to choose some of these based on results for time integration methods. As preconditioners, we consider SGS preconditioners based on flux vector splitting discretizations with a cutoff function for small eigenvalues. We compare these methods based on a discrete Fourier analysis. Numerical results on pitching and plunging airfoils identify AW3 as the best smoother regarding overall efficiency. Specifically, for the NACA 64A010 airfoil steady-state convergence rates of as low as 0.85 were achieved, or a reduction of 6 orders of magnitude in approximately 25 pseudo-time iterations. Unsteady convergence rates of as low as 0.77 were achieved, or a reduction of 11 orders of magnitude in approximately 70 pseudo-time iterations.

Jeremy Morton, Freddie D. Witherden, Antony Jameson et al.

The design of flow control systems remains a challenge due to the nonlinear nature of the equations that govern fluid flow. However, recent advances in computational fluid dynamics (CFD) have enabled the simulation of complex fluid flows with high accuracy, opening the possibility of using learning-based approaches to facilitate controller design. We present a method for learning the forced and unforced dynamics of airflow over a cylinder directly from CFD data. The proposed approach, grounded in Koopman theory, is shown to produce stable dynamical models that can predict the time evolution of the cylinder system over extended time horizons. Finally, by performing model predictive control with the learned dynamical models, we are able to find a straightforward, interpretable control law for suppressing vortex shedding in the wake of the cylinder.