Convergence performance of the approximate factorization methods with multi-block implicit boundary conditions at hypersonic speeds

Koca, Melikşah
This thesis study presents convergence characteristics of the implicit approximate factorization methods at hypersonic flow conditions and with 2-dimensional and 3-dimensional geometries. The efficiency of the implicit boundary conditions at block interfaces for the multi-block grids is investigated for different approximate factorization methods. Standard Alternating Direction Implicit (ADI) method, Diagonal Dominant Alternating Direction Implicit method (DDADI) with and without Huang’s sub-iteration correction, Spatially Factored with Diagonal Time terms (SFDT) method which CFL3D open-source code uses as an approximate factorization method and Diagonal Dominant Spatialy Factored with Diagonal Time terms (DDSFDT) method which is developed for this study with and without Huang’s sub-iteration correction are used to obtain tridiagonal matrices on the left-hand side while solving compressible Reynolds-averaged Navier-Stokes equations. Residual histories and total run time of the analyses are compared for compression ramp, Sajben Transonic Diffuser, double wedge, and 2 and 3-dimensional Apollo Command Module geometries. DDADI and DDSFDT with Huang’s sub-iteration correction methods showed the best convergence characteristics in terms of residual history for 2 dimensional simple cases. However, the total run time is higher compared to the SFDT method. ADI method has the slowest convergence rates in general. For 3 dimensional Apollo Command Module, SFDT methods gave the best-converged solution. For diagonal dominant relaxation schemes maximum allowable CFL numbers decreased with implicit boundary conditions on block interfaces. However, at equal CFL numbers convergency improved. Implicit boundary conditions improved the convergence performance of the Standard ADI method dramatically, maximum allowable CFL numbers are increased for multi-block grids. SFDT method with implicit boundary conditions eliminates the errors caused by the multi-block treatment and the maximum allowable CFL number is increased for the 2-dimensional Apollo Command Module. However, for the other cases, maximum allowable CFL numbers remained the same despite the elimination of the errors caused by the multi-block explicit boundary conditions treatment. It is shown that the diagonal dominance of the approximate factorization method directly affects the efficiency of the implicit boundary condition treatment for the block interfaces of the multi-block grids. It is concluded that convergence characteristics of the approximate factorization methods and efficiency of the multi-block implicit boundary conditions are related and case-dependent. Hence, it is concluded that having multiple solution algorithm options in the solver is a great advantage.


Implementation Studies of Robot Swarm Navigation Using Potential Functions and Panel Methods
Merheb, Abdel-Razzak; GAZİ, VEYSEL; Sezer Uzol, Nilay (2016-10-01)
This paper presents a practical swarm navigation algorithm based on potential functions and properties of inviscid incompressible flows. Panel methods are used to solve the flow equations around complex shaped obstacles and to generate the flowlines, which provide collision-free paths to the goal position. Safe swarm navigation is achieved by following the generated streamlines. Potential functions are used to achieve and maintain group cohesion or a geometric formation during navigation. The algorithm is i...
Elliptical Pin Fins as an Alternative to Circular Pin Fins for Gas Turbine Blade Cooling Applications Part 2 Wake Flow Field Measurements and Visualization Using Particle Image Velocimetry
Uzol, Oğuz (null; 2001-06-07)
Extensive wake flow field measurements and visualizations are conducted using particle image velocimetry (PIV) inside the wakes of the elliptical and circular pin fin arrays in order to better understand the flow physics and the loss mechanisms of these devices. The true-mean velocity field inside the wake two diameters downstream of the pin fin arrays is obtained by collecting and ensemble averaging a large number of PIV samples in the midplane of the test section. Additional experiments are also conducted...
Convergence acceleration based on convergence error estimation
Eyi, Sinan (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...
Pressure-velocity coupling algorithm-based pressure reconstruction from PIV for laminar flows
Gunaydinoglu, Erkan; Kurtuluş, Dilek Funda (Springer Science and Business Media LLC, 2020-01-01)
In this study, we propose a method to reconstruct pressure fields from planar particle image velocimetry measurements for laminar flows by employing semi-implicit method for pressure-linked equations algorithm to solve governing equations where measured velocities are inherently used as boundary conditions. The method starts with interpolating the measured velocity field on a staggered computational grid. The continuity equation, in the form of pressure equation for incompressible flows, is solved with this...
Direct Calculation of Entropy Generation by Solving Reynolds-Averaged Entropy Transport Equation in an Air-Cooled Turbine Cascade
Orhan, Omer Emre; Uzol, Oğuz (2012-06-15)
This paper presents an implementation of directly solving Reynolds-Averaged Entropy Transport equation as a part of the CFD solution to predict entropy generation rates in a two-dimensional turbine blade stator section. The Reynolds Averaged Entropy Transport and the necessary modeling. equations are implemented to a commercial CFD solver as a User Defined Scalar (UDS). The results are compared with those obtained by post-processing the temperature and velocity fields obtained by solving full Navier-Stokes ...
Citation Formats
M. Koca, “Convergence performance of the approximate factorization methods with multi-block implicit boundary conditions at hypersonic speeds,” M.S. - Master of Science, Middle East Technical University, 2022.