Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since 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 KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

STATE-AND-TRANSITION MODELING AND ADAPTIVE MANAGEMENT: TOOLS FOR FUTURE CO-DEVELOPMENT OF MADAGASCAR’S NATURAL RESOURCES AND PEOPLE

Madagascar’s terrestrial and aquatic ecosystems have long supported a unique set of ecological communities, many of whom are endemic to the tropical island. Those same ecosystems have been a source of valuable natural resources to some of the poorest people in the world. Nevertheless, with pride, ingenuity and resourcefulness, the Malagasy people of the southwest coast, being of Vezo identity, subsist with low development fishing techniques aimed at an increasingly threatened host of aquatic seascapes. Mangroves, sea grass bed, and coral reefs of the region are under increased pressure from the general populace for both food provisions and support of economic opportunity. Besides purveyors and extractors, the coastal waters are also subject to a number of natural stressors, including cyclones and invasive, predator species of both flora and fauna. In addition, the aquatic ecosystems of the region are undergoing increased nutrient and sediment runoff due, in part, to Madagascar’s heavy reliance on land for agricultural purposes (Scales, 2011). Moreover, its coastal waters, like so many throughout the world, have been proven to be warming at an alarming rate over the past few decades. In recognizing the intimate interconnectedness of the both the social and ecological systems, conservation organizations have invoked a host of complimentary conservation and social development efforts with the dual aim of preserving or restoring the health of both the coastal ecosystems and the people of the region. This paper provides a way of thinking more holistically about the social-ecological system within a resiliency frame of understanding. Secondly, it applies a platform known as state-and-transition modeling to give form to the process. State-and-transition modeling is an iterative investigation into the physical makeup of a system of study as well as the boundaries and influences on that state, and has been used in restorative ecology for more than a decade. Lastly, that model is sited within an adaptive management scheme that provides a structured, cyclical, objective-oriented process for testing stakeholders cognitive understanding of the ecosystem through a pragmatic implementation and monitoring a host of small-scale interventions developed as part of the adaptive management process. Throughout, evidence of the application of the theories and frameworks are offered, with every effort made to retool conservation-minded development practitioners with a comprehensive strategy for addressing the increasingly fragile social-ecological systems of southwest Madagascar. It is offered, in conclusion, that the seascapes of the region would be an excellent case study worthy of future application of state-and-transition modeling and adaptive management as frameworks for conservation-minded development practitioners whose multiple projects, each with its own objective, have been implemented with a single goal in mind: preserve and protect the state of the supporting environment while providing for the basic needs of the local Malagasy people.