##Reference data from "Benchmark Computations of Laminar Flow Around a Cylinder" 
##of Schäfer & Turek from 1996 ( 2D-Q1 test case)
##                L_a(recirculation length)     deltaP 
## lower bound    0.0842                        0.1172
## upper bound    0.0852                        0.1176
##
## our numerical results
## deltaP = P(0.15,0.2)-P(0.25,0.2)
## Recirculation length, L_a = x_r - x_a, 
##                       x_r - end of recirculation, 
##                       x_a - start of recirculation( x_a = 0.25, which is at end of cylinder)
## Here, x_r = average position of negative and positive x-velocity(recirculation end)
## and x_a1  = 1st fluid barycenter with negative x-velocity (L_a1)
## x_a2 = cylinder boundary = 1st fluid barycenter with negative x-velocity (L_a1) - dx/2
##
## lattice inflow velocity, u_in_L = 0.05
## physical inflow velocity, u_max = 0.3 m/s, u_mean = 0.2 m/s
## omega for different resolution
## nHeight    omega
## 50         1.7699115044248
## 100        1.6
## 150        1.4598540145985
## 200        1.3422818791946
## 300        1.1494252873563
## 400        1.010101010101
#unknowns    l/h   nHeight    outlet_BC     L_a1           L_a2                deltaP  
12359        5     50         expol         0.0861         0.082               0.1181412    
12359        5     50         dnt           0.0861         0.082               0.1181412                   
12359        5     50         pab           0.0861         0.082               0.1184088                   
12359        5     50         eq            0.0861         0.082               0.1184076    

49488        5     100        expol         0.08815        0.0861              0.1198788    
49488        5     100        dnt           0.08815        0.0861              0.1198776
49488        5     100        pab           0.08815        0.0861              0.1198752                         
49488        5     100        eq            0.08815        0.0861              0.1198752                         

111373       5     150        expol         0.086100005    0.0847333383333     0.1212804    
111373       5     150        dnt           0.086100005    0.0847333383333     0.1212804    
111373       5     150        pab           0.086100005    0.0847333383333     0.1212792    
111373       5     150        eq            0.086100005    0.0847333383333     0.1212792 

198043       5     200        expol         0.085075       0.08405             0.1173504
198043       5     200        dnt           0.085075       0.08405             0.1173504
198043       5     200        pab           0.085075       0.08405             0.117348
198043       5     200        eq            0.085075       0.08405             0.117348

445653       5     300        expol         0.08541667     0.0847333366667     0.1183068
445653       5     300        dnt           0.08541667     0.0847333366667     0.1183032
445653       5     300        pab           0.08541667     0.0847333366667     0.1183056
445653       5     300        eq            0.08541667     0.0847333366667     0.118308

792342       5     400        expol         0.0845625      0.08405             0.1174836 
792342       5     400        dnt           0.0845625      0.08405             0.1174848
792342       5     400        pab           0.0845625      0.08405             0.1174836
792342       5     400        eq            0.0845625      0.08405             0.117486
