Solving the Couette inverse problem using a wavelet-vaguelette decomposition
This paper develops a new approach to computing the shear rate from the torque and rotationalvelocity measurements in a Couette rheometer. It is based on wavelet-vaguelette decomposition (WVD) proposed by Donoho (Donoho, D., Appl. Comput. Harmon. Anal. 2, 101–126 1995). This decomposition consists in expanding the shear rate into a truncated wavelet series, whose coefficients can be determined by computing the inner products of the wavelet functions with dual functions svagueletted. Compared to other strategies used for recovering the shear rate such as Tikhonov regularization, the WVD method exhibits greater accuracy and faster convergence. Because of the spatial adaptivity of wavelets, it still performs well when the flow curve is irregular syield stress, sudden behavior change, etc.d and thus no prior knowledge of the shear rate characteristics se.g., existence of a yield stress, smoothnessd is needed. Its efficiency is demonstrated by applying the method to two fluids sa polymeric gel and a granular suspensiond.