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Schmid, Manuel Florian

University of British Columbia

In the atmospheric boundary-layer (ABL), both the turbulent flow dynamics of the air and the structure of the surface below are complex and multi-scale. This dissertation aims to strengthen the theoretical and computational foundation for models that attempt to account for an increasing amount of this complexity. First, the relationship between one-dimensional profiles and the three-dimensional flow field is examined for urban-like geometry. The thesis makes the case that mean profiles, which generally involve explicit or implicit spatial averaging, are best understood as a special case of the volume averaging methodology that was developed in the context of flow through porous media. The two natural definitions of the volume average both have some convenient and some inconvenient properties. The thesis discusses these properties and how they affect the analysis and modelling of urban flow profiles, potentially resulting in leading-order errors if not handled correctly. Next, the computation of momentum budgets is discussed for simulations relying on the immersed-boundary method, where a non-smooth flow field encompasses both fluid and solid regions. The thesis argues that budgets should nonetheless be free of residuals if their computation closely follows the methods used during the simulation. Using a concrete example, it is shown how small numerical details can produce non-negligible contributions, how the handling of forcing terms and boundary nodes can be resolved by careful analysis, and how some ambiguity might have to be tolerated for terms that are derived with mathematical identities that do not hold exactly for discrete data. Finally, a new code for ABL flow simulations is presented. The code is designed for improved adaptability since simulation methods often have to be tailored to the surface geometry and other problem properties. To achieve this goal without sacrificing performance or correctness, the code is written in the high-level, high-performance language Julia, makes use of extensive automated tests, and relies on experience with earlier implementations to clean up the mathematical formulation and implementation of the methods. The code is shown to match numerical results and performance properties of existing codes, and early experience has shown first benefits of the enhanced adaptability.

Text

2022-11-23

Attribution 4.0 International

http://hdl.handle.net/2429/83286

Civil Engineering

University of British Columbia

UBCV

http://creativecommons.org/licenses/by/4.0/