A Chebyshev-Legendre Spectral Method for the Transient Solutions of Flow Past a Solid Sphere

✍ Scribed by Hoa D. Nguyen; Jacob N. Chung

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 431 KB
• Volume: 104
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1993.1032

✦ Synopsis

A full spectral model for the stream-function-vorticity formulation is developed for the solution of unsteady flow past a rigid sphere. To convert the governing partial differential equations to discrete form, Chebyshev and Legendre polynomials are employed to expand the vorticity and stream function in the radial and angular directions, respectively, together with a first-order, fully implicit, iterative scheme for time advancement. The solution to the system of discrete nonlinear equations is accomplished by LU decomposition in conjunction with the influence matrix to resolve the lack of vorticity boundary conditions. Owing to the global nature of the orthogonal trial functions, the present technique provides a means to achieve highly accurate results with less number of unknowns than either traditional finite difference or finite element methods. Comparisons of numerical solutions with previous results show consistent trends as reported in studies dealing with Cartesian coordinates. (C) 1993 Academic Press. Inc.