Adaptive Techniques for Scale-Resolving Turbulence Simulations Using Super-Resolution Reconstruction

Abstract

Accurate prediction of turbulent flow phenomena is an area of keen engineering interest. Predicting these phenomena, such as flow separation, remains difficult after decades of research. The Reynolds averaged Navier-Stokes (RANS) equations are commonly used, but rely on empirical models that can fail to accurately predict interesting phenomena like separation. Direct numerical simulation (DNS) would solve all the shortcomings of the RANS equations, but it is not practical on modern machines at Reynolds numbers of engineering interest. Large-eddy simulation (LES) is a crucial middle ground that is becoming increasingly useful as computational power grows. LES relies on empirical models for small-scale flow features that are computationally expensive to capture, but still resolves larger turbulent features. While small-scale modeling brings practical turbulence simulations just within reach of modern machines, these simulations remain expensive. Adaptation can increase the practicality of LES by further reducing its computational cost.

This dissertation implements an adaptive method for LES in a discontinuous Galerkin (DG) context. The core of the adaptation process is a neural-network that predicts fine scales in a given flow-field. Preliminary testing in 1D shows reconstruction is accurate with a simple neural-network. Reconstruction remains accurate in two and three dimensions using simple network architectures. Preliminary testing on more sophisticated network architectures indicates significant gains in reconstruction accuracy are possible. A single super-resolution network trained on a variety of data is used to reconstruct various flows during adaptation. Two error indicators are proposed based on super-resolution reconstruction. One is based on the magnitude of the network's fine scale correction and the other on an entropy-adjoint weighted residual. The error indicators are tested by adapting a variety of turbulent flow problems.

The adaptive method outperforms uniform refinement given a poor initial mesh. The adaptive methods are tested on a channel flow problem where no initial mesh refinement is assumed. The simple correction magnitude error indicator returns the expected error pattern across Reynolds numbers. Adaptation with this indicator proceeds as expected, placing the most resolution near the channel walls, while leaving the channel center unrefined. The entropy-adjoint weighted residual indicator shows more noise using the same averaging process. The extra noise decreases as Reynolds number increases. Adaptation with the correction magnitude indicator generally outperforms uniform refinement on this case, achieving similar performance to uniform refinement at approximately 25% fewer degrees of freedom. The correction magnitude indicator is then tested against a mean velocity gradient indicator. Testing on a periodic hill geometry shows similar results between the error indicators. The indicators show high error near the center of the domain, as opposed to the already refined domain edges. Adaptation performance is more similar to uniform refinement on this case. Finally, a modified version of the simple correction magnitude indicator is tested on a geometry intended to mimic a trailing edge cooling slot in turbomachinery. A tendency toward wake refinement continues from the periodic hill test case. Once again, the adapted results are in line with, or slightly better than, uniform refinement on a degree of freedom basis. Suggestions are made to improve the performance of the weighted residual error indicator with different averaging techniques. Suggestions are also made for impactful alternative research directions.