Reduced-Hermite bifold-interpolation assisted schemes for the simulation of random wind field

Interpolation techniques have been recently introduced to enhance the computational efficiency of the classical spectral representation method (SRM) in the simulation of random ergodic fluctuations in turbulence. However, the conventional interpolation assisted scheme (IAS) is not efficient enough to cater for cases with a large number of simulation points, where the computational demand of the Cholesky decomposition makes them less attractive. In this study, reduced-Hermite based bifold-interpolation assisted schemes (BIAS), which incorporate the reduced-Hermite interpolation in a bifold-interpolation scheme, are developed to further enhance the efficiency of SRM. The reduced-Hermite interpolation reduces the number of Cholesky decompositions in BIAS to half of that required by the conventional Hermite interpolation. The adoption of the bifold-interpolation technique fixes the number of Cholesky decompositions, thus eliminating the Cholesky decomposition as a cause for effecting the efficiency of SRM. Specifically, BIAS is further classified as the sequential BIAS (SeBIAS) that uses Hermite or reduced-Hermite interpolation and the synchronous BIAS (SyBIAS) based on a 2D reduced-Hermite interpolation, each highlighted by their respective merits. A parametric analysis is conducted to investigate the computational efficiency and associated modeling error of BIAS, which are also compared to those of conventional IAS and traditional SRM. The findings suggest that reduced-Hermite SyBIAS is the scheme of choice with higher computational efficiency and smaller modeling bias than other cases. In addition, it is a robust method in which the modeling error is not sensitive to the interpolation of the second part of the double-index frequency. The effectiveness of the wind samples generated by the reduced-Hermite SyBIAS is verified via a case study. Moreover, the results are compared to those from the proper orthogonal decomposition (POD) based approach, which proves that the reduced-Hermite SyBIAS offers a faster and more expedient simulation of random wind fields.