Publication: An adaptive wavelet collocation method for fluid-structure interaction at high Reynolds numbers

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Title	An adaptive wavelet collocation method for fluid-structure interaction at high Reynolds numbers
Authors/Editors*	N. Kevlahan, O. Vasilyev
Where published*	SIAM J. Sci. Comput.
How published*	Journal
Year*	2005
Volume	26
Number	6
Pages	1894-1915
Publisher	xxxxx
Keywords
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Abstract	Two mathematical approaches are combined to calculate high Rey-nolds number incompressible fluid--structure interaction: a wavelet method to dynamically adapt the computational grid to flow intermittency and obstacle motion, and Brinkman penalization to enforce solid boundaries of arbitrary complexity. We also implement a wavelet based multilevel solver for the Poisson problem for the pressure at each time step. The method is applied to two-dimensional flow around fixed and moving cylinders for Reynolds numbers in the range $3 imes 10^1 le Re le 10^5$. The compression ratios up to 1,000 are achieved. For the first time it is demonstrated in actual dynamic simulations that the compression scales like $Re^{1/2}$ over five orders of magnitude, while computational complexity scales like $Re$. This represents a significant improvement over the classical complexity estimate of $Re^{9/4}$ for two-dimensional turbulence.