Learning Dominant Urban Flows around High-Rise Buildings with Data-Driven Balance Models

Abstract

This thesis develops a data-driven dominant balance model to recognise and cluster the flow pattern blowing through a high-rise building in an urban area under neutral atmospheric conditions. To be consistent with the governing equation used in simulations, the Reynolds-Averaged Navier-Stokes (RANS) equation is selected as the governing equation. It is divided into six sub-parts based on the physical meanings of each term in RANS. The time-averaged simulation results are used as the data set basis for further machine learning and clustering. The approach used to achieve the final dominant balance models consists of knowledge from fluid mechanics, statistics and programming. Knowledge from fluid mechanics is mainly used for proposing governing equations and interpreting the final outcomes, whereas the knowledge from programming is used for script writing and program running. Finally, the knowledge from statistics is the key for algorithms to achieve the clustering and dominant balance model acquirement. This approach includes the finite difference method, Gaussian mixture models (GMM), singular value decomposition and sparse principal component analysis (SPCA). The finite difference method is used for approximating the derivatives in RANS, which works as a post-processing step. GMM are trained by using randomly subsampled points and applied for the clustering of the processed data points. A drawback of yielding overlapping and trivial clusters of GMM is spotted and SPCA is applied as the solution to trivial results, using regularisation to proceed with a sparse approximation for excessive cluster elimination. The final data-driven dominant balance models are obtained and visualised by generating two tables for two cases.