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Multilevel methods for temporal and spatial flow transition simulation in a rough channel
Author(s) -
Liu Zhining,
Liu Zhixing,
Liu Chaoqun,
McCormick Steve
Publication year - 1994
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650190104
Subject(s) - multigrid method , instability , open channel flow , mathematics , compressibility , grid , mechanics , mathematical analysis , geometry , flow (mathematics) , physics , partial differential equation
We 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.