The use of non-intrusive reduced order modeling (NIROM) to approximate high-fidelity computer models has been steadily increased over the past decade. Recently, local NIROM has been proposed to improve the model accuracy in highly nonlinear problems in which distinct characteristic regimes coexist. The core concept of local NIROM is the decomposition of the parameter domains into a subregime to create multiple models. However, the existing local NIROM not only partitions the individual models in a mutually exclusive manner, but also uses a single model for prediction. This results in the extrapolation of surrogate models and the generation of artificial discontinuities. To mitigate these problems, a local NIROM that allows flexible overlapping of individual NIROMs is developed. This method softly partitions and combines individual NIROMs using machine learning techniques, such as fuzzy c-means and multinomial logistic regression. Furthermore, a variance-based adaptive sampling technique that can consider both local exploitation and global exploration is applied to improve model accuracy. The proposed method is validated against the transonic flow and in-flight icing problem, and demonstrates superior performance relative to its local counterpart by up to 16.5% and 33.9% in terms of normalized root-mean-square error and exclusive OR error, respectively.
<div class="section abstract"><div class="htmlview paragraph">Diagonalized alternating-direction implicit (DADI) method is implemented in the Eulerian hyperbolic droplet solver, ICEPAC, for efficient high-order accurate analysis of aircraft icing. Detailed techniques for implementing the DADI method considering hyperbolicity characteristics are discussed. For the Eulerian droplet equation system to be strictly hyperbolic, additional source terms regarding artificial droplet pressure are included. Validations of the present implicit solver are conducted using two- and three-dimensional steady benchmark tests: NACA0012 airfoil, NACA23012 airfoil, and a swept wing. Also, the oscillating airfoil SC2110 case was analyzed to verify the robustness and efficiency of the proposed solver. In addition, the computational cost of the current implicit solver is considerably lower than that of the explicit multi-stage solver.</div></div>
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