High-fidelity Large-Eddy Simulation (LES) of fluid flow over complex terrain has long been a challenging computational problem. Complex terrain leads to increased velocity gradients, turbulence production, and complex turbulent wakes. Body-fitted grids need a high resolution to deal with additional effects of highly skewed cells that follow a terrain of steep slope. Immersed boundary methods need special techniques like wall models to numerically resolve the associated drag force. In flow over complex terrain, the characteristic scale decreases locally which makes it a challenging endeavour for LES to mimic the turbulent energy cascade, particularly when steep terrain produce vortices and streaky structures that sustain turbulence away from the surface. This thesis presents the canopy stress method in which the terrain is immersed into the fluid, cutting the cells of a Cartesian grid, where the effects of terrain are treated by the form drag and the skin friction drag. Heat transfer analysis of flow in pipes and porous media is considered to study the sensitivity of canopy drag coefficients. A scale-adaptive methodology is proposed to model the subgrid-scale terrain effects. The analysis of wind tunnel measurements over mountains and forests shows that the scale-adaptive model dynamically adjusts the dissipation rate by the scale of energetic eddies near complex terrain. In regions without terrain effects, where subgrid turbulence is locally isotropic, the model also provides accurate dissipation rate. These results suggest that combining the rotation tensor and the vortex stretching vector with the strain tensor through the second-invariant of the square of the velocity gradient tensor is a novel approach to improve the fidelity of LES over complex terrain in which the dissipation becomes scale-aware; i.e. the rate of turbulence dissipation is adjusted with the changes in the characteristic scales. The numerical analysis of four distinct flow regimes (e.g., Chapters 3-6) illustrates the accuracy, simplicity, and cost-effectiveness of the proposed LES methodology.

Forest canopies cover about 30% of the land surfaces some of which are hilly or mountainous. Both complex terrain and forest canopies influence mean flow and turbulence, playing a critical role in affecting momentum and scalar transfer. Although recent advances have been made in numerical simulations of canopy flows, few have been conducted over steep slope terrain and considered full sets of physical and physiological processes in sub-canopy layers, which greatly limits our understanding of canopy flows and scalar transfer. To address this limitation, we upgrade the Weather Research and Forecasting model with the large-eddy simulations module (WRF-LES) by incorporating the immersed-boundary method (IBM) to improve the simulations over steep slope terrain. In addition, an advanced multiple layer canopy module (MCANOPY) is developed based largely on the Community Land Model version 4.5 and coupled with WRF-LES to simulate sources and/or sinks of momentum, heat, water vapor, and CO2 across multiple canopy layers. Both IBM and MCANOPY are evaluated against field measurements, demonstrating good performances compared with observations. The updated modeling system (i.e., WRF-LES-IBM-MCANOPY) is then applied over a forest edge to investigate the effects of foliage distributions and scalar distributions on canopy flows and scalar transfer. The results show that foliage distributions have a significant impact on the flow dynamics and scalar transfer, mainly due to the sub-canopy jet. The scalar distributions affect the scalar field with the ground source being the most important. The modeling system also simulates flows over forested hills. Flow dynamics over a three-dimensional hill show a different feature to those over a two-dimensional hill, where much large turbulence structures are simulated in the lee of a three-dimensional hill. Simulations over different slope hills demonstrate significant impacts of slopes. The lee side turbulence is enhanced as the hill slope increases. A new flow feature is the nearly unvarying flow field within the canopy in the lee of a steep slope hill, subjected to the influence of foliage distributions. Our upgraded WRF-LES-IBM-MCANOPY system has demonstrated promising capacities in many applications such as wind-turbine siting, wildfire propagation prediction, and interpretation of eddy covariance data over complex landscapes.

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.

A three-dimensional immersed boundary method was implemented into a Large Eddy Simulation (LES) with advanced subgrid-scale modeling capability. In this way, obstacles in the urban atmospheric boundary layer such as buildings and hills could be represented without changing the Cartesian grid. These numerical methods are applied in two urban environment investigations. The first explores the effect of hilly urban morphology on dispersion characteristics in the urban boundary layer. The second investigate the application of wall functions for building convection heat transfer in large eddy simulation. Air flow and dispersion in urban areas are strongly affected by the presence of buildings. In natural settings hills strongly impact dispersion. Five simulations of flow over building arrays over flat terrain and witch of Agnesi hills with maximum slope of 0.26 were conducted to study turbulence and dispersion properties in and above the canopy. While the small hill reduces the shear stress and velocity variance above the urban canopy compared to the flat urban array, the shear stress increases for larger hills. The TKE in the canopy downwind of the hill decreased below the value for the flat urban case, but canopy ventilation for the hilly cases was several times larger than for the flat case, especially near the hill crest. Therefore, urban dispersion models should account for these relatively moderate terrain changes to produce accurate results. In urban energy balance models, convection heat transfer model is often over-simplified by using a uniform convection heat transfer coefficient (CHTC) for each building surface. We consider more complex flow patterns by implementing a wall function to calculate the local CHTC from local velocities provided by LES. Simulations consisting of single building, 3 x 3 building arrays and 6 x 6 building arrays with neutral and unstable conditions were performed. Validation showed similar results as a low Reynolds number simulation resolving the viscous region, but both simulations disagreed with measurements in a wind tunnel. The log-law relation, which is a fundamental assumption underlying many wall models, was found to be accurate for the roof surface velocity and temperature for high building density, but it does not apply to windward and leeward surfaces. Density of buildings also acts as one of most important factors in determining the temperature distribution and buoyancy force in the urban canyon and roughness layer.