##Reference data from "Benchmark Computations of Laminar Flow Around a Cylinder" 
##of Schäfer & Turek from 1996 ( 2D-Q2 test case)
##                Stroudal number(St)           deltaP 
## lower bound    0.2950                        2.4600
## upper bound    0.3050                        2.5000
##
## our numerical results
## deltaP = P(0.15,0.2)-P(0.25,0.2)
## Stroudal number. St = fD/u_mean,
##                  where, f - frequency of separation (measured from velocityY signal over time)
##                         D - diameter of the cylinder
##                         u_mean  - mean velocity
##
## This datas are obtained using acoustic scaling i.e keeping lattice inflow velocity constant and 
## changed omega for different resolution. The value used for simulation are given below.
## lattice inflow velocity, u_in_L = 0.05
## physical inflow velocity, u_max = 1.5 m/s, u_mean = 1.0 m/s
## omega for different resolution
## nHeight    omega
## 50         1.9493177387914
## 100        1.9047619047619
## 150        1.8621973929236
## 200        1.8214936247723
## 300        1.7421602787456
## 400        1.6722408026756
###################################################################################################################
##outlet_BC  : expol 
###################################################################################################################
##nHeight  unknowns   l/h       freq(f)        St                       deltaP 
    ##                                                         min           max           average
  50       4859         2       2.8568367675  0.2856836768     2.08434 2.84709 2.49615953073
  50       7359         3       2.8568367675  0.2856836768     2.416311 2.512755 2.46631526237
  50       12359        5       2.8568367675  0.2856836768     2.419653 2.506239 2.46551112894
                                
  100      19488        2       2.8568367675  0.2856836768     2.341866 2.609358 2.49199818591
  100      29488        3       2.8568367675  0.2856836768     2.474319 2.524329 2.49644952474
  100      49488        5       2.8568367675  0.2856836768     2.458647 2.542395 2.49789131484
                                
  150      43873        2       2.6782844695  0.267828447      2.41023 2.649345 2.54857488756
  150      66373        3       3.2139413634  0.3213941363     2.515263 2.589519 2.55310341679
  150      111373       5       3.2139413634  0.3213941363     2.501559 2.607189 2.55369244078
                                
  200      78043        2       2.8568367675  0.2856836768     2.379063 2.544651 2.47694323538
  200      118043       3       2.8568367675  0.2856836768     2.454834 2.511567 2.48287936282
  200      198043       5       2.8568367675  0.2856836768     2.43399 2.532543 2.48420144978
                                              
  300      175653       2       3.2139413634  0.3213941363     2.385639 2.521623 2.46150178111
  300      265653       3       3.2139413634  0.3213941363     2.436438 2.506683 2.47440242729
  300      445653       5       3.2139413634  0.3213941363     2.421132 2.525904 2.4731561949
           
  400      312342       2       2.8568367675  0.2856836768     2.394672 2.509851 2.46407087706
  400      472342       3       2.8568367675  0.2856836768     2.431221 2.505966 2.4700605982
  400      792342       5       2.8568367675  0.2856836768     2.415615 2.526063 2.47008124438
###################################################################################################################
##outlet_BC  : dnt 
###################################################################################################################
##nHeight  unknowns   l/h       freq(f)        St                       deltaP 
    ##                                                         min           max           average
  50       4859         2        0 0                           unstable    
  50       7359         3        0 0                           unstable   
  50       12359        5        0 0                           unstable                 
                                 
  100      19488        2        2.8568367675  0.2856836768    2.380713 2.569161 2.49080161019
  100      29488        3        2.8568367675  0.2856836768    2.470638 2.52771 2.49692241829
  100      49488        5        2.8568367675  0.2856836768    2.457672 2.543634 2.49789376012
                                             
  150      43873        2        0 0                           unstable                 
  150      66373        3        3.2139413634  0.3213941363    2.512524 2.592447 2.5534482009
  150      111373       5        3.2139413634  0.3213941363    2.500371 2.608023 2.55356528336
                                             
  200      78043        2        2.8568367675  0.2856836768    2.404425 2.526285 2.47829328336
  200      118043       3        2.8568367675  0.2856836768    2.453103 2.513445 2.48309974363
  200      198043       5        2.8568367675  0.2856836768    2.433942 2.532441 2.48423118441
                                 
  300      175653       2        3.2139413634  0.3213941363    2.405901 2.508201 2.46397882609
  300      265653       3        3.2139413634  0.3213941363    2.43528 2.50779 2.47469877811
  300      445653       5        3.2139413634  0.3213941363    2.420754 2.525736 2.47329002699
           
  400      312342       2        2.8568367675  0.2856836768    2.411334 2.499708 2.46460162069
  400      472342       3        2.8568367675  0.2856836768    2.430384 2.506917 2.4701764093
  400      792342       5        2.8568367675  0.2856836768    2.415489 2.525931 2.4698981919
###################################################################################################################
##outlet_BC  : eq 
###################################################################################################################
##nHeight  unknowns   l/h       freq(f)        St                       deltaP 
    ##                                                         min           max           average
  50       4859         2       2.8568367675  0.2856836768     2.232744 2.681334 2.47884158921
  50       7359         3       2.8568367675  0.2856836768     2.418063 2.500842 2.46635688456
  50       12359        5       2.8568367675  0.2856836768     2.422758 2.506038 2.46586416042
                                                               
  100      19488        2       2.8568367675  0.2856836768     2.388561 2.567301 2.49103471964
  100      29488        3       2.8568367675  0.2856836768     2.470728 2.528457 2.49694666567
  100      49488        5       2.8568367675  0.2856836768     2.458689 2.542329 2.49774667316
                                                               
  150      43873        2       2.6782844695  0.267828447      2.452794 2.614524 2.54415326237
  150      66373        3       3.2139413634  0.3213941363     2.512623 2.592327 2.55343007496
  150      111373       5       3.2139413634  0.3213941363     2.500983 2.607135 2.55347024738
                                                               
  200      78043        2       2.8568367675  0.2856836768     2.409816 2.522994 2.47836426987
  200      118043       3       2.8568367675  0.2856836768     2.453124 2.513346 2.48310727436
  200      198043       5       2.8568367675  0.2856836768     2.434572 2.531724 2.484151991
                                                               
  300      175653       2       3.2139413634  0.3213941363     2.409711 2.506122 2.46435233583
  300      265653       3       3.2139413634  0.3213941363     2.435325 2.507724 2.47470371214
  300      445653       5       3.2139413634  0.3213941363     2.421177 2.525406 2.47330586357
                                                               
  400      312342       2       2.8568367675  0.2856836768     2.414571 2.49798 2.46465913493
  400      472342       3       2.8568367675  0.2856836768     2.430423 2.507097 2.47017274963
  400      792342       5       2.8568367675  0.2856836768     2.415789 2.525544 2.46986698051
###################################################################################################################
##outlet_BC  : pab 
###################################################################################################################
##nHeight  unknowns   l/h       freq(f)        St                           deltaP 
##                                                             min           max           average
  50       4859         2       2.8568367675  0.2856836768     2.298546 2.610213 2.46897443478
  50       7359         3       2.8568367675  0.2856836768     2.418762 2.506284 2.4673990075
  50       12359        5       0 0                            unstable                                                    
                                                               
  100      19488        2       2.8568367675  0.2856836768     2.423316 2.542434 2.49212782159
  100      29488        3       2.8568367675  0.2856836768     2.468391 2.530926 2.49740872564
  100      49488        5       2.8568367675  0.2856836768     2.45754 2.543817 2.49779051424
                                                               
  150      43873        2       3.2139413634  0.3213941363     2.482788 2.593926 2.54783738681
  150      66373        3       3.2139413634  0.3213941363     2.510802 2.594013 2.55385633883
  150      111373       5       3.2139413634  0.3213941363     2.499846 2.608032 2.55349151424
                                                               
  200      78043        2       2.8568367675  0.2856836768     2.431449 2.509776 2.47926608546
  200      118043       3       2.8568367675  0.2856836768     2.452005 2.514795 2.48332815892
  200      198043       5       2.8568367675  0.2856836768     2.434626 2.531502 2.48415676612
                                                               
  300      175653       2       3.2139413634  0.3213941363     2.425371 2.496687 2.46670234033
  300      265653       3       3.2139413634  0.3213941363     2.434545 2.508804 2.47494994753
  300      445653       5       3.2139413634  0.3213941363     2.421222 2.525154 2.47340492954
                                                               
  400      312342       2       2.8568367675  0.2856836768     2.427399 2.490645 2.46536813943
  400      472342       3       2.8568367675  0.2856836768     2.429862 2.507988 2.47026915742
  400      792342       5       2.8568367675  0.2856836768     2.416011 2.5251 2.469737006

