Fast simulation of nonstationary wind velocity fields by proper orthogonal decomposition interpolation

Abstract

The classic spectral representation method (SRM) has been extensively utilized in simulating nonstationary wind velocity fields because of its great precision and simplicity. However, this method is computationally expensive when it is applied to the situation with a great number of simulation positions. Although several attempts have been made to alleviate the computational burden, the efficiency improvement may be limited. To this end, this study develops a proper orthogonal decomposition (POD) interpolation-enhanced approach to expedite the simulation of nonstationary wind fields by SRM. Firstly, the Cholesky decomposition is only executed for the spectral matrices at time-frequency interpolation points and the corresponding computational cost is therefore reduced greatly. The POD interpolation is then used to approximately decouple each decomposed spectrum into a small amount of time and frequency functions, thereby invoking the fast Fourier transform to speed up the summing of cosine functions. The POD operation is merely executed for the low-dimensional matrix and the interpolation operation solely aims at the few time and frequency functions. As a result, the proposed approach has the potential to considerably improve the simulation efficiency. Finally, numerical examples with the simulation of two different nonstationary wind fields validate its precision and efficiency.