Effect of mesh distortion on the accuracy of high order vorticity-velocity CFD approaches

The numerical solution of the incompressible Navier-Stokes equations offers an alternative to experimental analysis of fluid-structure interaction (FSI). We would save a lot of time and effort and help cut back on costs, if we are able to accurately model systems by these numerical solutions. These advantages are even more obvious when considering huge structures like bridges, high rise buildings or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the Kinematic Laplacian Equation (KLE) to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ordinary differential equations (ODE) time integration schemes, allowing us to tackle each problem as a separate module. The current algortihm for the KLE uses an unstructured quadrilateral mesh, formed by dividing each triangle of an unstructured triangular mesh into three quadrilaterals for spatial discretization. This research deals with determining a suitable measure of mesh quality based on the physics of the problems being tackled. This is followed by exploring methods to improve the quality of quadrilateral elements obtained from the triangles and thereby improving the overall mesh quality. A series of numerical experiments were designed and conducted for this purpose and the results obtained were tested on different geometries with varying degrees of mesh density.

INVESTIGATING THE IMPACTS OF STREAMBED HABITAT HETEROGENEITY ON ECOSYSTEM STRUCTURE AND PROCESSES USING BASIC AND APPLIED PERSPECTIVES

Stream restoration often focuses on increasing habitat heterogeneity to reverse ecosystem degradation. However, the connection between heterogeneity and ecosystem structure and processes is poorly understood. We looked to investigate this interaction from both applied and basic science perspectives. For the applied study, we examined two culvert replacements designed to mimic natural stream channels, to see if they were better at maintaining ecosystem processes within as well as upstream and downstream of culverts compared to non-replaced culverts. We measured three ecosystem processes (nutrient uptake, hydrologic characteristics, and coarse particulate organic matter retention) and found that stream simulation culvert restoration improved organic matter retention within culverts, and that there were no differences in processes measured upstream and downstream of both restoration designs. Our results suggest that measurements of ecosystem processes are more likely to show a response to restoration if they match the scale of the restoration activity. For the basic science study, we quantified the longitudinal spatial heterogeneity of physical and biofilm characteristics at microhabitat to segment scales on streams with different streambed variability. We found that all physical characteristics and biofilm characteristics were spatially independent at the macro-habitat scale and greater. Together, these studies demonstrate the importance of scale in ecological interactions and the value of incorporating considerations of scale into restoration activities.