Chebyshev spectral solution of viscous flow with corner singularities
Two flow problems are studied using spectral methods: the stability of two-dimensional Rayleigh convection in a box (with weak corner singularities) and the driven-cavity problem (with strong corner singularities). Compared to the usual stream function/vorticity formulation, the single fourth-order equation for stream function used here requires half the number of coefficients for this formulation and does not require iterative treatment of boundary conditions. The Rayleigh-convection stability problem represents a self-adjoint system. Three different spectral methods are used. A true Galerkin procedure is required to avoid spurious eigenvalues and obtain accurate results. It was found that poor convergence of pseudospectral coefficients is caused by a Runge-like phenomenon near the walls. However, the weaker singularity in the Rayleigh-convection problem does not need to be treated specifically. An overdetermined pseudospectral method was developed, with special consideration of corner singularities, for a two-dimensional viscous flow problem. The rate of convergence is greatly improved by subtracting the strongest corner singularities.
- Research Organization:
- Michigan Univ., Ann Arbor (USA)
- OSTI ID:
- 7059180
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
Similar Records
Traps and snares in eigenvalue calculations with application to pseudospectral computations of ocean tides in a basin bounded by meridians
Analysis of interaction effect of stress intensity factors for interface cracks and angular corners using singular integral equations of the body force method