Özet:
In this thesis, Incompressible Smoothed Particle Hydrodynamics (ISPH) technique is implemented to analyze various convective-diffusive transport problems numerically. First of all, a brief summary of applications and developments in SPH is given. Then, SPH methodology is presented. A detailed discussion on frequently used high order SPH approximation schemes is made and an expansion of existing projection methods developed for isothermal flow to non-isothermal and double-diffusive flows is introduced. The code developed during this thesis study is validated for isothermal problems such as lid-driven cavity and vortex spin-down. Furthermore, in order to test the upper limit of accuracy of SPH computations, a grid-based ISPH approach is proposed. Grid-based ISPH is applied to natural convection in a square cavity problem and the results are compared to the data available in the literature. Similar to gridbased ISPH code, meshless ISPH code is used to solve natural convection problems. Rayleigh-B́enard convection is studied and multiple states of the solutions are obtained. Moreover, natural convection is investigated at the onset of instability in which multicellular and oscillatory flow patterns are observed. Apart from natural convection, ISPH code also introduced to double-diffusive transport problems. In terms of doublediffusion, ISPH performance in aiding and opposing flows are provided. Furthermore, ISPH code is also implemented to two-phase flows. In the context of two-phase flows, topological changes of the interfaces and Rayleigh-Taylor instability problems are simulated. ISPH results for two-phase flow are compared to results obtained by Level Set Method.
