Thomas Lichtenegger

A simple, data-assisted and physics-based approach for recurrent fluid dynamics is presented, and approximations for the application to macroscopic problems are developed. Large-step predictions are built upon sufficiently similar reference states in a precomputed database around which the Navier–Stokes equations are linearized. Hence, the deviation of any flow field from its nearest reference state obeys a linear propagator, and its evolution over a large time step can be calculated by the convolution with this propagator. An efficient, Gaussian approximation for these operators is constructed from their leading-order moments, which can be obtained along with the set of reference states with little overhead costs. The methodology is applied to two- and three-dimensional vortex shedding after a cylinder at Re = 200. Validation is carried out via a comparison of field time series, temporal means and variances, autocorrelation functions at selected locations, and global balances of momentum and kinetic energy. Results for cases with boundary conditions outside the reference set are of mostly (very) good accuracy, with speed-ups of about two orders of magnitude compared to classical computational fluid dynamics simulations. While the propagator simulations do not reach real-time capability for large-scale, three-dimensional flows, they might serve as a data augmentation method in connection with machine learning approaches.

Particle deposition on an object from a turbulent flow is of considerable interest in many applications. Numerical predictions using conventional computational fluid dynamics (CFD) are challenging due to that a large number of individual deposition events must be observed over a long time for the deposition statistics to converge. Here, we investigate the potential for using recurrence CFD (rCFD) to efficiently and accurately predict particle deposition on a cylinder for Reynolds numbers (Re) in the interval 20≤Re≤10 000. We quantify the front- and back-side deposition efficiencies independently, analyze the locations and timings of deposition events, and benchmark the computational performance. We find that rCFD predicts deposition efficiencies with similar accuracy as the corresponding CFD simulations, but at a fraction of the computational cost. The most significant deposition occurs on the front side of the cylinder and is very well described for all Reynolds numbers investigated. For Re=10 000, we observe a dependence on the rCFD database length in the prediction of the much less effective back-side deposition, as the database only contains a limited subset of the more rare flow behaviors responsible for this deposition. These results can be used to accelerate particle deposition studies by several orders of magnitude, which would bring significant benefits for computationally challenging applications, such as sensor soiling in the car industry, icing on aircraft, and ash build-up in boilers.