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.

Active surgical positioning device for a cochlear implant electrode array

Cochlear implants have been of great benefit in restoring auditory function to individuals with profound bilateral sensorineural deafness. The implants are used to directly stimulate auditory nerves and send a signal to the brain that is then interpreted as sound. This project focuses on the development of a surgical positioning tool to accurately and effectively place an array of stimulating electrodes deep within the cochlea. This will lead to improved efficiency and performance of the stimulating electrodes, reduced surgical trauma to the cochlea, and as a result, improved overall performance to the implant recipient. The positioning tool reported here consists of multiple fluidic chambers providing localized curvature control along the length of the attached silicon electrode array. The chambers consist of 200μm inner diameter PET (polyethylene therephthalate) tubes with 4μm wall thickness. The chambers are molded in a tapered helical configuration to correspond to the cochlear shape upon relaxation of the actuators. This ensures that the optimal electrode placement within the cochlea is retained after the positioning tool becomes dormant (for chronic implants). Actuation is achieved by injecting fluid into the PET chambers and regulating the fluidic pressure. The chambers are arranged in a stacked, overlapping design to provide fluid connectivity with the non-implantable pressure controller and allow for local curvature control of the device. The stacked tube configuration allows for localized curvature control of various areas along the length of the electrode and additional stiffening and actuating power towards the base. Curvature is affected along the entire length of a chamber and the result is cumulative in sections of multiple chambers. The actuating chambers are bonded to the back of a silicon electrode array.