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Renewable energy technologies can help us combat climate change and hydrokinetic energy conversion systems could play a major role. The simplicity of hydrokinetic devices helps us to exploit renewable sources, especially in remote locations, which is not possible with conventional methods. A new type of hydrokinetic device called the Energy Conveyor Belt was designed, which works on the concept of conveyor belt technology. Numerical simulations are performed on the design of the Energy Conveyor Belt with Ansys FLUENT to optimize its performance. Some of the optimized models produced a maximum power slightly above 1 kW. The numerical results are then compared to the experimental results of other hydrokinetic turbines. The compactness and flexibility of the design give the Energy Conveyor Belt an advantage over other hydrokinetic devices in regions with fluctuating water levels. Further research has to be undertaken into cascading systems to increase the overall power generated by the system.

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A finite volume method with grid adaption is applied to two hyperbolic problems: the ultra-relativistic Euler equations, and a scalar conservation law. Both problems are considered in two space dimensions and share the common feature of moving shock waves. In contrast to the classical Euler equations, the derivation of appropriate initial conditions for the ultra-relativistic Euler equations is a non-trivial problem that is solved using one-dimensional shock conditions and the Lorentz invariance of the system. The discretization of both problems is based on a finite volume method of second order in both space and time on a triangular grid. We introduce a variant of the min-mod limiter that avoids unphysical states for the Euler system. The grid is adapted during the integration process. The frequency of grid adaption is controlled automatically in order to guarantee a fine resolution of the moving shock fronts. We introduce the concept of "width refinement" which enlarges the width of strongly refined regions around the shock fronts; the optimal width is found by a numerical study. As a result we are able to improve efficiency by decreasing the number of adaption steps. The performance of the finite volume scheme is compared with several lower order methods.