AN ADAPTIVE WAVELET COLLOCATION METHOD FOR FLUID–STRUCTURE INTERACTION AT HIGH REYNOLDS NUMBERS

Abstract. Two mathematical approaches are combined to calculate high Reynolds number in-compressible fluid–structure interaction: a wavelet method to dynamically adapt the computational grid to flow intermittency and obstacle motion, and Brinkman penalization to enforce solid bound-aries 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 3×101 ≤ Re ≤ 105. 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 Re1/2 over five orders of magnitude, while computational complexity scales like Re. This represents a significant improvement over the classical complexity estimate of Re9/4 for two-dimensional turbulence. Key words. Turbulence, wavelets, fluid–structure interaction AMS subject classifications. 76F65, 76D25, 65T60 1. Introduction. On