Chebyshev collocation methods in thermoconvective problems

• Published in: The European physical journal. ST, Special topics Vol. 146; no. 1; pp. 235 - 247
• Main Author: Herrero, H.
• Format: Journal Article
• Language: English
• Published: 01-07-2007
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2007-00183-x

Chebyshev collocation methods are high-order methods. This means that high precision is obtained with low-order expansions. Then 'small' matrices appear in the numerical implementation and reduced computing resources become necessary. Thermoconvective fluid dynamics problems are large ones, involving various partial differential equations for several fields in large dimensions. The models present a number of difficulties, such as the different orders of derivatives for the different fields, or lack of information on the boundary conditions for pressure. This paper presents a review of the specific characteristics of this method when it is applied to thermoconvective problems: the method, the types of problems, the different resulting models, the strategies to overcome the difficulties of the different derivative orders and the characteristics of the matrices, and the convergence properties. A comparison of its efficiency with other numerical methods like finite differences and finite elements is included.