Yazar "Cete, Ali Ruhsen" seçeneğine göre listele

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    Öğe
    Alternating Cell Direction Implicit Method using Approximate Factorization on Hybrid Grids
    (Global Science Press, 2022) Cete, Ali Ruhsen; Onay, Oguz Kaan
    In this study, a novel fast-implicit iteration scheme called the alternating cell direction implicit (ACDI) method is combined with the approximate factorization scheme. This application aims to offer a mathematically well-defined version of the ACDI method and to increase the accuracy of the iteration scheme used for the numerical solutions of partial differential equations. The ACDI method is a fast-implicit method that can be used for unstructured grids. The use of fast implicit iteration methods with unstructured grids is not common in the literature. The new ACDI method has been applied to the unsteady diffusion equation to determine its convergence and time-dependent solution ability and character. The numerical tests are conducted for different grid types, such as structured, unstructured quadrilateral, and hybrid polygonal grids. Second, the ACDI was applied to the unsteady advection-diffusion equation to understand the time-dependent and progression capabilities of the presented method. Third, a full potential equation solution is created to understand the complex flow solving ability of the presented method. The results of the numerical study are compared with other fast implicit methods, such as the point Gauss-Seidel (PGS) and line Gauss-Seidel (LGS) methods and the fourth-order Runge-Kutta (RK4) method, which is an explicit scheme, and the Laasonen method, which is a fully implicit scheme. The study increased the abilities of the ACDI method. Due to the new ACDI method, the approximate factorization method, which is used only in structural grids that are known to be advantageous, can be applied to any mesh structure.
  • [ X ]
    Öğe
    Approximate Factorization Method Using Alternating Cell Direction Implicit Method: Comparison of Convergence Characteristics Using Basic Model Equations
    (Academic Publication Council, 2021) Cete, Ali Ruhsen
    In this paper, a fast implicit iteration scheme called the alternating cell directions implicit (ACDI) method is combined with the approximate factorization scheme. The use of fast implicit iteration methods with unstructured grids is hardly. The proposed method allows fast implicit formulations to be used in unstructured meshes, revealing the advantages of fast implicit schemes in unstructured meshes. Fast implicit schemes used in structured meshes have evolved considerably and are much more accurate and robust, and are faster than explicit schemes. It is a crucial novel development that such developed schemes can be applied to unstructured schemes. In steady incompressible potential flow, the convergence character of the scheme is compared with the Runge-Kutta order 4 (RK4), Laasonen, point Gauss-Seidel iteration, old version ACDI, and line Gauss-Seidel iteration methods. The scheme behaves like an approximation of the fully implicit method (Laasonen) up to an optimum pseudo-time-step size. This is a highly anticipated result because the approximate factorization method is an approach to a fully implicit formulation. The results of the numerical study are compared with other fast implicit methods (e.g., the point and line Gauss-Seidel methods), the RK4 method, which is an explicit scheme, and the Laasonen method, which is a fully implicit scheme. The study increased the accuracy of the ACDI method. Thus, the new ACDI method is faster in unstructured grids than other methods and can be used for any mesh construction.