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Naive scheme

The maximum values of system parameters changing with time are shown in Table 1. From the table, we can see that the amplitude of the maximum values grow rapidly soon after computation. By step 34, infinity appears in the data. Much smaller \(\Delta x\) and \(\Delta t\) also have been tested and a similar result is achieved. So it is evident that this naive scheme can not be used on this problem.


Step No.  Max_Velocity    Max_Pressure    Max_Energy      Max_Density
     0    0.35427         1.0000          2.5000          1.0000
     1    0.68467         1.0000          2.5000          1.0000
     2    0.97869         1.0000          2.5000          1.0000
     3    1.2311          1.0000          2.5001          1.0000
     4    1.4431          1.0001          2.5002          1.0000
     5    1.6196          1.0001          2.5003          1.0001
     6    1.7673          1.0002          2.5006          1.0002
     7    1.8932          1.0003          2.5008          1.0002
     8    2.0039          1.0004          2.5011          1.0003
     9    2.1051          1.0005          2.5013          1.0004
    10    2.2022          1.0004          2.5012          1.0004
    11    2.3005          1.0002          2.5009          1.0002
    12    2.4057          1.0000          2.5001          1.0000
    13    2.5247          1.0000          2.5001          1.0000
    14    2.6671          1.0001          2.5001          1.0000
    15    2.8473          1.0001          2.5002          1.0001
    16    3.0896          1.0001          2.5002          1.0001
    17    3.4399          1.0001          2.5003          1.0001
    18    3.9998          1.0001          2.5003          1.0001
    19    5.0521          1.0001          2.5003          1.0001
    20    7.8292          1.0001          2.5003          1.0001
    21    44.564          3.9459          7.1151          1.0000
    22    5.2499          4.0312          9.5749          1.0000
    23    3.5772          4.1917          10.195          1.0000
    24    3.2152          4.4466          10.858          1.0000
    25    3.1844          4.8249          11.671          1.0000
    26    3.1865          5.3721          12.694          1.0063
    27    3.2260          6.2313          15.420          1.0379
    28    13.182          7.8516          19.508          1.1229
    29    6.9411          9.6998          24.181          1.3086
    30    5.5236          12.033          30.069          1.5379
    31    8.0931          14.833          37.065          1.8182
    32    15.825          18.477          45.862          2.1634
    33    26.677          31.812          79.214          2.5856
    34    Inf             Inf             Inf             Inf
    35    Inf             Inf             Inf             Inf
    36    Inf             Inf             Inf             Inf
    37    0.39059E+06     Inf             Inf             0.41689E+33
    38    0.97190E+06     Inf             Inf             0.13968E+34
Table 1. Output of maximum variables of naive scheme