In the present study, an implicit and adaptive Nonlinear Frequency Domain method (pNLFD) has been implemented to the Navier-Stokes equations on deformable grids. Although the computational time for periodic flows is drastically reduced by using the NLFD approach over classical time marching schemes, implementing the pNLFD concept leads to an even faster numerical algorithm. Besides that, the need for a large amount of memory, which is the main disadvantage of the NLFD method, is resolved in the present pNLFD approach. Moreover, the concept of dynamic or moving/deformable grid, which is a need in many problems dealing with periodic flows, is extended to the pNLFD method. Finally, in order to accelerate the convergence, the nonlinear LU-SGS technique which is an implicit time marching method, is implemented. In the LU-SGS technique the cells are treated locally, hence its implementation is quite suitable for the pNLFD method, where different cells have different number of modes and therefore has to be treated individually. Results are presented for 2D stationary, oscillating and pitching cylinders and are compared with previous numerical results as well as experimental data.
An innovative implicit approach for the adaptive Nonlinear Frequency Domain method (adaptive NLFD) has been introduced for the Navier-Stokes equations on deformable grids. It has been shown that for a periodic flow problem, a huge reduction in the computational costs and a spectral temporal accuracy of the results could be achieved by solving the flow governing equations in the frequency instead of the time domain. This computational efficiency may be even further enhanced through an adaptive modal augmentation of the Fourier series representing the local flow solution. In the present study, to accelerate the convergence rate, an innovative modified nonlinear LU-SGS technique is proposed, where the modes are updated in a segregate fashion. The unique and important outcome of this implementation is that the computational efficiency of the solver does not decrease as the number of modes increases. Results are presented for the laminar vortex shedding behind a stationary cylinder, a stationary transonic airfoil, and a plunging airfoil and are compared with previous numerical results as well as experimental data.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.