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.


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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.