An Adaptive Wavelet Collocation Method for Fluid-Structure Interaction at High Reynolds Numbers

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 $3\times 10^1 \le Re \le 10^5$. The compression ratios of up to 1000 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.