Multilevel methods for temporal and spatial flow transition simulation in a rough channel Journal Article

Overview

AbstractWe investigate the instability of 2D incompressible flows in a rough planar channel by tracking the growth of the unstable mode in its early stage. We develop both second‐ and fourth‐order finite difference methods on a staggered grid, together with a fully implicit time‐marching scheme, using grid generation to accommodate fairly general geometries. A multigrid full approximation scheme based on the line‐distributive relaxation method is used for fast convergence. For a 2D smooth channel, numerical results show good agreement with the analytic solution obtained from linear theory for small disturbances. Numerical results for a 2D channel with one and two roughness elements are analysed by Fourier analysis. They show how the roughness elements affect the growth of the perturbation.