A WPOD-Kriging Reduced-Order Method for Parametric CFD Simulations

Abstract

High-fidelity computational fluid dynamics (CFD) simulation usually carries a heavy computational burden, especially for parametric CFD simulations requiring multiple calculations. To address this challenge, researchers have developed reduced-order modeling (ROM) to significantly decrease the computational burden by building a simplified model. This article proposes a hybrid method of weighted proper orthogonal decomposition and Kriging, a novel reduced-order method. This method improves the accuracy of the reduced-order model by assigning appropriate weights to the samples while estimating the specific design parameters. The main innovation of this work is the development of the optimized method for generating the weights. Firstly, the leave-one-out method is employed to divide the samples into the training set and test set, and the multivariate Gaussian distribution is used to convert the Euclidean distance between the training set and test set into weight. Then, we adopt the WPOD-Kriging method to construct a reduced-order model using the training set. This model is compared with the test set to obtain the error. By repeatedly resetting the training set and the test set, we receive multiple errors and average them to calculate the global error. This process involves an important parameter, which is the covariance matrix of multivariate Gaussian distribution. We can generate the optimal covariance matrix by minimizing the global error to achieve the optimized method for generating the weights. The efficacy of the WPOD-Kriging method is validated through three parametric CFD simulations. Compared to other similar approaches, the proposed method offers a more accurate reduced-order model.