Grafik işleme birimi üzerinde yüksek mertebe kompakt şema kullanılarak gömülü sınır uygulaması

Computational Fluid Dynamics (CFD) has become a major tool for simulating the fluid flow in various areas. It is a cost and time effective way compared to experimental methods. Even though it is not always possible to obtain realistic solutions concerning complex high Reynolds number flows due to the hardware problems, numerous researches have been dedicated to find ways to overcome this shortness. Numerical methods that are used to perform CFD analyses define the accuracy and duration of simulations. For instance, in order to get accurate results with low order numerical methods, very high grid resolution is required and high grid resolution yields to long computation periods with high memory usage. To overcome this drawback higher order schemes are used commonly to get reliable solutions with coarser grids. Spectral methods are more reliably than standart finite difference methods but the computational cost of these schemes are very high. Compact higher order finite difference schemes have spectral like resolution ability but simpler structure. Compared to the standart finite difference schemes, compact schemes use smaller stencil and give better resolution with the same order of accuracy. In this study a sixth order compact scheme is used to obtain results of several incompressible flow test cases; flow over a flat plate, lid driven cavity flow and flow around a circular cylinder. Mesh generation is another time consuming part of CFD simulations. As an alternative to the body-fitted meshes, immersed boundary method (IBM) which is a very efficient and straightforward way to generate grid has been used widely. With IBM one does not need to generate mesh that conforms the body, but change the algorithm of the solution to impose the boundaries. In this method a simple mesh such as cartesian mesh is generated without the body and then in the solution step the presence of the body is introduced by the modifications of the governing equations. Compared to body-fitted structured or unstructured grids, in IBM less memory is required and grid generation is very easy. An IB method is applied in the test cases of this thesis study to represent solid boundaries. Another achievement of this study is that it uses a graphics processing unit (GPU) as a computational platform. General purpose computing on GPUs has recently become a very efficient way compared to central processing unit (CPU) in computational sciences. The computations of the present study are performed on one of NVIDIA's scientific computing GPUs Tesla C1060 which has 30 streaming multi-processors, each containing 8 scalar processors clocked at 1.3 GHz with a bandwith of 102 GB/s to 4 GB GDDR3 global memory. NVIDIA‟s Compute Unified Device Architecture (CUDA) toolkit which is a complete software development solution for programming CUDA-enabled GPUs is utilized as the code design medium. In conclusion, three test cases, flow over a flat plate, lid driven cavity flow and flow around a circular cylinder, are solved using immersed boundary method and sixth order compact finite difference scheme on a GPU. Results obtained from flow over a flat plate test case are compared to Blasius boundary layer theorem solutions. Lid driven cavity flow and flow around a circular cylinder results are compared to the ones found on literature. All results obtained in this study are in very good agreement with theoritical and reference results.