Convergence acceleration based on convergence error estimation

2013-01-01
New methods are developed for convergence error estimation and convergence acceleration in iteratively solved problems. The convergence error estimation method is based on the eigenvalue analysis of linear systems, but it can also be used for nonlinear systems. Newton's method is used to estimate the magnitude and the phase angle of eigenvalues. The convergence of iterative method is accelerated by subtracting convergence error from the iteratively calculated solutions. The performances of these methods are demonstrated for the Laplace, Euler and Navier-Stokes equations.

Suggestions

Convergence Error Estimation and Convergence Acceleration in Iteratively Solved Problems
Eyi, Sinan (null; 2012-07-09)
New methods are developed for convergence error estimation and convergence acceleration in iteratively solved problems. The convergence error estimation method is based on the eigenvalue analysis of linear systems, but it can also be used for nonlinear systems. The convergence of iterative method is accelerated by subtracting convergence error from the iteratively calculated solutions. The performances of these methods are demonstrated for the Laplace, Euler and NavierStokes equations.
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...
Implicit lattice boltzmann method for laminar/turbulent flows
Çevik, Fatih; Albayrak, Kahraman; Department of Mechanical Engineering (2016)
Lattice Boltzmann Method is an alternative computational method for fluid physics problems. The development of the method started in the late 1980s and early 1990s. Various numerical schemes like stream and collide, finite difference, finite element and finite volume schemes are used to solve the discrete Lattice Boltzmann Equation. Almost all of the numerical schemes in the literature are explicit schemes to exploit the natural features of the discrete Lattice Boltzmann Equation like parallelism and easy c...
A 2-0 navier-stokes solution method with overset moving grids
Tuncer, İsmail Hakkı (1996-01-01)
A simple, robust numerical algorithm to localize moving boundary points and to interpolate uniteady solution variables across 2-D, arbitrarily overset computational grids is presented. Overset 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 parameters of the search algorithm give the interpolation weights at the localized boundary point. The method is independent of nu...
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 ...
Citation Formats
S. Eyi, “Convergence acceleration based on convergence error estimation,” 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/69342.