적합직교분해 기법에서의 효율적인 스냅샷 선정을 위한 고유값 분석

다국어 초록 (Multilingual Abstract)

The guideline of selecting the number of snapshot dataset, N<SUB>s</SUB> in proper orthogonal decomposition(POD) was presented via the analysis of Eigen values based on the singular value decomposition(SVD). In POD, snapshot datasets from the solutions of Euler or Navier-Stokes equations are utilized to SVD and a reduced order model(ROM) is constructed as the combination of Eigen vectors. The ROM is subsequently applied to reconstruct the flowfield data with new set of flow conditions, thereby enhancing the computational efficiency. The overall computational efficiency and accuracy of POD is dependent on the number of snapshot dataset; however, there is no reliable guideline of determining N<SUB>s</SUB>. In order to resolve this problem, the order of maximum to minimum Eigen value ratio, O(R)from SVD was analyzed and presented for the decision of N<SUB>s</SUB>: in case of steady flow, N<SUB>s</SUB> should be determined to make O(R) be 10<SUP>9</SUP>. For unsteady flow, N<SUB>s</SUB> should be increased to make O(R) be 10<SUP>11~12</SUP>. This strategy of selecting the snapshot dataset was applied to two dimensional NACA0012 airfoil and vortex flow problems including steady and unsteady cases and the numerical accuracies according to N<SUB>s</SUB> and O(R) were discussed.

참고문헌 (Reference)

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