Approximate factorization using ACDI method on hybrid grids and parallelization of the scheme

Onay, Oğuz Kaan
In this thesis study, a fast implicit iteration scheme called Alternating Cell Directions Imp licit method is combined with Approximate Factorization scheme. This application aims to offer a mathematically well defined version of the Alternating Cell Directions Implicit Method and increase the accuracy of the iteration scheme that is being used for the numerical solutions of the partial differential equations. The iteration scheme presented here is tested using unsteady diffusion equation, Laplace equation and advection-diffusion equation. The accuracy, convergence character and the stability character of the scheme compared with suitable iteration schemes for structured and unstructured quadrilateral grids. Besides, it is shown that the proposed scheme is applicable to triangular and hybrid polygonal grids. A transonic full potential solver is generated using the current scheme. The flow around a 2-D cylinder is solved for subcritical and supercritical cases. Axi-symmetric flow around cylinder is selected as a benchmark problem since the potential flow around bodies with a blunt leading edge is a more challenging problem than slender bodies. Besides, it is shown that, the method is naturally appropriate for parallelization using shared memory approach without using domain decomposition applications. The parallelization that is performed here is partially line, partially point parallelization. T he performance of the application is presented for a 3-D unsteady diffusion problem using Cartesian cells and 2-D unsteady diffusion problem using both structured and unstructured quadrilateral cells.


Numerical methods for multiphysics flow problems
Belenli Akbaş, Mine; Kaya Merdan, Songül; Rebholz, Leo G.; Department of Mathematics (2016)
In this dissertation, efficient and reliable numerical algorithms for approximating solutions of multiphysics flow problems are investigated by using numerical methods. The interaction of multiple physical processes makes the systems complex, and two fundamental difficulties arise when attempting to obtain numerical solutions of these problems: the need for algorithms that reduce the problems into smaller pieces in a stable and accurate way and for large (sometimes intractable) amount of computational resou...
Inverse Sturm-Liouville Systems over the whole Real Line
Altundağ, Hüseyin; Taşeli, Hasan; Department of Mathematics (2010)
In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization t...
Development of an incompressible navier-stokes solver with alternating cell direction implicit method on structured and unstructured quadrilateral grids
Baş, Onur; Tuncer, İsmail Hakkı; Department of Aerospace Engineering (2007)
In this research, the Alternating Cell Direction Implicit method is used in temporal discretisation of the incompressible Navier-Stokes equations and compared with the well known and widely used Point Gauss Seidel scheme on structured and quadrilateral unstructured meshes. A two dimensional, laminar and incompressible Navier-Stokes solver is developed for this purpose using the artificial compressibility formulation. The developed solver is used to obtain steady-state solutions with implicit time stepping m...
Numerical method for optimizing stirrer configurations
Schafer, M; Karasözen, Bülent; Uludağ, Yusuf; YAPICI, KEREM; Uğur, Ömür (2005-12-15)
A numerical approach for the numerical optimization of stirrer configurations is presented. The methodology is based on a parametrized grid generator, a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The flow solver is based on the discretization of the Navier-Stokes equations by means of the finite-volume method for block-structured, boundary-fitted grids with multi-grid acceleration and parallelization by grid partitioning. The optimization tool is an ...
A 2-D unsteady Navier-Stokes solution method with overlapping/overset moving grids
Tuncer, İsmail Hakkı (1996-01-01)
A simple, robust numerical algorithm to localize intergrid boundary points and to interpolate unsteady solution variables across 2-D, overset/overlapping, structured computational grids is presented. Overset/ overlapping grids are allowed to move in time relative to each other. The intergrid boundary points are localized in terms of three grid points on the donor grid by a directional search algorithm. The final parameters of the search algorithm give the interpolation weights at the interpolation point. Th...
Citation Formats
O. K. Onay, “Approximate factorization using ACDI method on hybrid grids and parallelization of the scheme,” M.S. - Master of Science, Middle East Technical University, 2013.