Abstract
The earlier chapters dealt with heat conduction problems, both steady and unsteady, mostly linear and occasionally nonlinear. However, a number of transport phenomena are influenced by fluid flow, and many of the interesting phenomena occur in closed geometries leading to “closed flows”. The reader will not come across anything new regarding spectral collocation techniques in this chapter. Much of what he has learnt earlier will find application. The important feature that will be the source of much discussion in this chapter is the decoupling of the pressure field from the velocity fields. This is due to the fact that the pressure in incompressible flows is viewed as a “slaved” variable.
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Notes
- 1.
Taking \(U_{lid}(x)=\left(1-x^{2q}\right)^2\) with large values of the integer \(q\) allows the lid velocity to approach \(1\) over a large part of the interval \(x\in [-1,1]\).
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Guo, W., Labrosse, G., Narayanan, R. (2012). 2D Closed Flow Problems: The Driven Cavity. In: The Application of the Chebyshev-Spectral Method in Transport Phenomena. Lecture Notes in Applied and Computational Mechanics, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34088-8_6
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