A computational fluid dynamics solver development for non-moving domain problems in FEniCS environment based on the residual-based variational multiscale method

This thesis presents the development of a Computational Fluid Dynamics (CFD) solver for non-moving domain problems in FEniCS, employing the Residual-Based Variational Multiscale (RBVMS) method. FEniCS is an open-source software library for solving differential equations using the finite element method, offering a powerful tool for scientific computing. The RBVMS method is employed for modeling flow in solving Navier-Stokes equations, with the objective of minimizing the effect of unresolved scales. This method aims to obtain more accurate results by using stabilization techniques to provide high accuracy and stability. In this thesis, the theoretical foundations of the RBVMS method are discussed in detail, and the implementation of this method on the FEniCS platform is explained. In order to evaluate the effectiveness and accuracy of the developed solver, two main test problems are studied: the lid-driven cavity problem and the flow around a rotating cylinder problem. These test problems are widely used in the literature and are considered ideal references for testing the accuracy of Computational Fluid Dynamics (CFD) solvers. In the analyses for the lid-driven cavity problem, the accuracy of the flow solutions was investigated using different mesh structures, Reynolds numbers, and obstacle geometries. Following the completion of the mesh independence studies, the optimal mesh density was determined, and the results obtained were compared with reference studies in the literature. The findings of these comparisons indicate that the developed solver accurately represents the flow characteristics and provides reliable results. For the flow problem around a rotating cylinder, flow structures and vortex dynamics are analyzed by using different values of the rotational speed of the cylinder. The results of these analyses demonstrated that the developed solver produces accurate and stable results even at high Reynolds numbers. Moreover, the flow characteristics obtained for different velocity ratios were found to be in good agreement with the reference data in the literature. This study makes an important contribution to the development of a CFD solver with the RBVMS method in FEniCS. The developed solver is considered an efficient and flexible tool that can be used in various engineering applications in still field problems. The findings of this study indicate the potential of FEniCS and the RBVMS method for broader applications in CFD.