Spectral algorithm for the analysis of flows in grooved channels

Abstract

SUMMARYA grid‐less, spectrally accurate algorithm for the analysis of flows in grooved channels is presented. The algorithm is based on the immersed boundary conditions concept, where the boundary conditions are submerged inside the computational domain and are treated as internal constraints. When grooves' ridges are orthogonal to the flow direction (transverse grooves), the flow remains two‐dimensional. As the grooves rotate away from this direction, the flow becomes three‐dimensional. An auxiliary coordinate system is defined in such a way that one of its axes is aligned with the grooves. It is shown that the governing equations expressed in this system decouple into a two‐dimensional flow across the grooves and a flow in the direction along the grooves, resulting in improved solution efficiencies. Fourier series are used for discretization in the direction transverse to the grooves and Chebyshev expansions for the direction across the channel. Special solvers that take advantage of the matrix structure have been implemented providing a significant acceleration of computation and reduction of memory requirements. Various tests have been conducted in order to illustrate the performance of the algorithm, to show its spectral accuracy and to characterize the effects of various numerical and physical parameters. Copyright © 2011 John Wiley & Sons, Ltd.