Revisiting the space-time gradient method: A time-clocking perspective, high order difference time discretization and comparison with the harmonic balance method

• DOI: 10.1016/j.cja.2022.05.016
• Publication Date: 2022-06-06T15:42:53Z
• Authors: Boqian WANG; Dingxi WANG; Mohammad RAHMATI; Xiuquan HUANG
• Keywords: Time derivative; Solver; Harmonic balance

This paper revisits the Space-Time Gradient (STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents from an alternative time-clocking perspective. The STG requires reordering blade passages according their relative clocking positions with respect blades adjacent row. As space-clocking is linked equivalent time-clocking, passage can be performed time-clocking. With perspective, flow solutions different same row are mapped at time instants or phase angles. Accordingly, derivative equation discretized in directly, more natural than transforming a spatial one as original method. To improve solution accuracy, ninth order difference scheme has been investigated discretizing derivative. achieve stable high scheme, implicit Lower-Upper Symmetric Gauss-Seidel/Gauss-Seidel (LU-SGS/GS) employed. NASA Stage 35 its blade-count-reduced variant used demonstrate validity based advantages Results existing harmonic balance solver also provided contrast two methods terms stability computational cost.