High-efficiency simulation of nonstationary wind velocity using diagonal POD of decomposed time-frequency interpolation node spectrum matrices

Abstract

The classical spectral representation method (SRM) used extensively to simulate nonstationary wind fields suffers from lower efficiency. Although some tries can already accelerate SRM, the efficiency improvement is restricted when the number of simulation points is large. For this reason, this paper proposed a high-efficiency interpolation scheme to boost the efficiency of SRM. Firstly, the decomposed time-frequency interpolation node spectrum matrices can be approximately decouple into the products of time and frequency functions using diagonal proper orthogonal decomposition (POD). Specifically, the POD operation is just for the diagonal elements, which are low-dimensional matrices. Since Cholesky decomposition is merely needed in the time-frequency interpolation point, the time consumed by spectral decomposition will be significantly reduced. Then, one-dimensional (1D) interpolation is implemented for these decoupling terms in the time and frequency directions, respectively. The decoupling results only contains a few time terms, so the number of 1D interpolation operations can be considerably decreased. Moreover, by exchanging the summation order, very few fast Fourier transform operations are required to accelerate harmonic superposition. Therefore, the proposed method may further enhance the simulation efficiency. Finally, through numerical examples, the accuracy and superiority of the proposed method are demonstrated.