Table 2: The results of different methods.

No. Dimensionless height from the top Numerical simulation result Mathematic model result Correction result
1 0.125 828.48 166.20 898.34
2 0.25 1381.84 1023.66 1511.75
3 0.375 2203.19 1881.10 2125.14
4 0.5 2896.51 2534.68 2534.68
5 0.625 3551.83 3595.92 3351.88
6 0.125 3011.31 2489.04 3221.18
7 0.25 3637.13 3028.95 3517.05
8 0.375 1552.94 1438.85 1682.90
9 0.5 2506.64 2396.56 2396.56
10 0.625 1667.51 1631.60 1387.56
11 0.125 2659.07 2046.79 2778.93
12 0.25 3680.77 2904.59 3392.68
13 0.375 3893.64 3444.55 3688.59
14 0.5 2362.48 2816.15 2816.15
15 0.625 906.29 1189.38 945.33
16 0.125 4324.76 4052.49 4784.63
17 0.25 2669.59 2462.41 2950.50
18 0.375 2328.41 1797.32 2041.37
19 0.5 2337.24 2396.15 2396.15
20 0.625 2850.94 3195.03 2950.98
21 0.125 4212.54 3610.27 4342.41
22 0.25 3363.36 2945.18 3433.27
23 0.375 4203.06 3802.97 4047.02
24 0.5 2212.92 2163.49 2163.49
25 0.625 2498.76 2752.85 2508.81