An Implicit Adaptive Non-Linear Frequency Domain Method (pNLFD) for Viscous Periodic Steady State Flows on Deformable Grids

Abstract

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.