Fig.1

Implementation process of correlation coefficient filtering method"

Fig.2

Change curve of the maximum relative error in database reconstruction with modal order"

Fig.3

Reconstruction error and correlation coefficient of one-dimensional Burgers equation with different model orders （U=0.4, μ=0.07, t=3.8）"

Fig.4

Accuracy of reconstructing one-dimensional Burgers equation using Gappy POD method varies with RP value"

Fig.5

Curves of maximum reconstruction error, average reconstruction error and correlation coefficient varying with α"

Table 1

Influence of point selection on the reconstruction accuracy of one-dimensional Burgers’ equation with different α decay rates （U = 0.4，μ = 0.07，t = 3.8）"

Table 2

Influence of point selection on the reconstruction accuracy of one-dimensional Burgers’ equation with different α decay rates （U = 1.3，μ = 0.13，t = 4.7）"

Fig.6

Gappy POD method reconstruction of one-dimensional Burgers’ equation waveform （U = 0.4，μ = 0.07，t = 3.8）"

Fig.7

Gappy POD method reconstruction of one-dimensional Burgers’ equation waveform（U = 1.3，μ = 0.13，t = 4.7）"

Fig.8

Reconstruction diagram of one-dimensional Burgers equation waveform"

Fig.9

Waveform reconstruction diagram of one-dimensional Burgers equation with waveform evolution over time"

Table 3

Impact of different point selection algorithms on reconstruction accuracy of Gappy POD method"

Fig.10

Illustration of lid-driven cavity flow"

Table 4

Validation of numerical model for lid-driven cavity flow"

Fig.11

Comparison between numerical solution and benchmark solution at Re=100"

Table 5

Number of different α values of point selection using the correlation coefficient filtering method"

Fig.12

Numerical solution of velocity field for lid-driven cavity flow at Re=800"

Fig.13

Reconstructed velocity fields using the Gappy POD method with point selection based on the correlation coefficient filtering method"

Fig.14

Relative error distribution of velocity field reconstruction using the Gappy POD method with point selection based on the correlation coefficient filtering method"

Table 6

Global error using the Gappy POD method with point selection based on correlation coefficient filtering method under different condition α values condition"

Table 7

Global reconstruction results of Gappy POD under different α values condition in a highly sparse database"

Table 8

Global reconstruction results of Gappy POD under different α values condition in a moderately sparse database"

Table 9

Reconstruction accuracy results of Gappy POD under different α values condition in a high density database"

Fig.15

Reconstruction of velocity field relative error distribution cloud map using Gappy POD method based on correlation coefficient filtering method for point selection"

Table 10

Comparison of reconstruction results using the correlation coefficient filtering method under different α settings"

Table 11

Comparison of reconstruction effects of two-dimensional lid-driven cavity flow with variable α setting"