Development of a canopy stress method for large eddy simulation over complex terrain

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