Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Experimental and Numerical Investigation of Piping in Uniform Embankment Dam With Weak Layer at the Upper Region(Izmir Institute of Technology, 2022) Okan, Merve; Tayfur, Gökmen; Bor Türkben, AslıFrom the past to nowadays, earth-fill dams have been built thanks to their advantages, however, piping is a problem that earth-fill dams can experience and then fail. While there are many studies about the overtopping failures of the dams, there are not too many surveys about dam failures due to piping. Dams having a height of 0.6 m, a bottom width of 2 m, and a crest width of 0.20 m were built in a channel of 1 m wide, 0.81 m high and 6.14 m long. 3 different scenarios have been created and the evolution of dam failure resulting from seepage at the dam was recorded by six cameras located at different locations. In the closed system, water was pumped from the lower reservoir to the upper channel. The dam was constructed by using a mixture consisting of 85 % sand and 15 % clay. A circular tunnel with a diameter of 2 cm was created at the middle or corner of the dam according to the scenario and at 6 cm below the dam crest. The breach areas at different time instants at upstream and downstream sides are determined by using the Gauss Area calculation method and by image processing, and then it has been found that methods give close values to each other. Breach discharge and time-varied velocity values were determined by using the continuity equation. Empirical relations were intended to be derived for the breach flow rate and empirical relations represented in the literature were trialed by using experimental findings.Master Thesis Computation of the Convection Diffusion Equation by the Fourth Order Compact Finite Difference Method(Izmir Institute of Technology, 2015) Bajellan, Asan Ali Akbar Fatah; Tayfur, GökmenThis dissertation aims to develop various numerical techniques for solving the one dimensional convection–diffusion equation with constant coefficient. These techniques are based on the explicit finite difference approximations using second, third and fourth-order compact difference schemes in space and a first-order explicit scheme in time. The suggested scheme has been seen to be very accurate and a relatively flexible solution approach in solving the contaminant transport equation for Pe ≤ 5. For the solution, the combined technique has been used instead of conventional solution techniques. The accuracy and validity of the numerical model are verified. The computed results showed that the use of the current method in the simulation is very applicable for the solution of the convection-diffusion equation. The technique is seen to be alternative to existing techniques. This dissertation is divided into six chapters: The derivation of the convective diffusion equation is given in Chapter 2. The main idea behind the higher order finite difference technique is given in Chapter 3. The numerical approximations to CDE described with ten different explicit schemes are introduced in Chapter 4. The results of numerical experiments using second, third and fourth-order compact difference schemes are presented in Chapter 5. Chapter 6 is devoted to a brief conclusion. Finally the references are introduced at the end.Master Thesis Convergence Analysis and Numerical Solutions of the Fisher's and Benjamin-Bono Equations by Operator Splitting Method(Izmir Institute of Technology, 2014) Zürnacı, Fatma; Tanoğlu, GamzeThis thesis is concerned with the operator splitting method for the Fisher’s and Benjamin-Bono-Mahony type equations. We showthat the correct convergence rates inHs(R) space for Lie- Trotter and Strang splitting method which are obtained for these equations. In the proofs, the new framework originally introduced in (Holden, Lubich, and Risebro, 2013) is used. Numerical quadratures and Peano Kernel theorem, which is followed by the differentiation in Banach space are discussed In addition, we discuss the Sobolev space Hs(R) and give several properties of this space. With the help of these subjects, we derive error bounds for the first and second order splitting methods. Finally, we numerically check the convergence rates for the time step ∆t.Master Thesis Uniformly Convergent Approximation on Special Meshes(Izmir Institute of Technology, 2007) Bingöl, Özgür; Neslitürk, Ali İhsanWe consider finite difference methods for the approximation of one-dimensional convection-diffusion problem with a small parameter multiplying the diffusion term. An analysis of the centered difference and upwind difference schemes on equidistant meshes shows that these methods are not uniformly convergent in the discrete maximum norm. However, we show that the upwind method over a set of suitably distributed mesh points produce uniformly convergent approximations in the discrete maximum norm. We further investigate the upwind difference method for the approximation of the convection-diffusion problem with a point source. Theoretical findings are supported with the numerical results.