A Parametric Modal Decomposition for Fluid Mechanics Problems

Abstract

Modal decomposition is widely used to simplify complex fluid mechanics problems by splitting the data set of the problem into different modes, which collect the main effects of the parameters involved in the problem. This data set is collected in a matrix form. Nevertheless, in case of the presence of more than two parameters affecting the system, a tensor multilinear modal decomposition should be applied. In this thesis, a brief development of matrix and tensor decomposition is addressed. In addition, multilinear modal decomposition is applied to perform a parametric study of an experimental flapping wing problem, where a large number of parameters can influence the system. Finally, it is obtained that the multilinear modal decomposition is a powerful method to simplify and extract the most significant features of a system. Since this method is only an experimental and mathematical method, it allows to extract the most relevant behaviors of each parameter without the necessity of entering into too much detail in the field of fluid mechanics.