StabFem Demo script for concentric jets WITH CONSTANT PROFILE.

Here we set Umax,2 = 1 for the outer jet and Umax,1 = 3/4 so that the ratio of MEAN VELOCITIES is the same as in the case of Poiseulle profile with Umax =1 for each jet

The arclength continuation is done in the plane (Re,beta) where beta is the "monitor" defined as beta = 100*int( ur* exp(-(x-2)^2 ). you can also use the energy as a monitor. For this just remove customized definitions of beta and dbetadu in SF_Custom.idp, the solver will switch to default ones.

NB :

- Using new generic interface - postprocessing is done completely from database exploration

Chapter 0 : Initialization
Chapter 1 : Generate a mesh and initial base flow
loop with increasing Re
plot last BF after this stage
Test Arclength
Generating the summary of Data Base for postprocessing
redraw figure from database
Plot last Base flow
compare with base flow for Re=30 from main branch

Chapter 0 : Initialization

close all;
addpath([fileparts(fileparts(pwd)), '/SOURCES_MATLAB']);
SF_Start('verbosity',4,'ffdatadir','./WORK_ArcLength_Constant/'); % NB use verbosity=2 for autopublish mode ; 4 during work
% SF_core_arborescence('cleanall'); % uncomment this line to clean database
SF_core_setopt('ErrorIfDiverge',false); % recommended option when using continuation mode
set(groot, 'defaultAxesTickLabelInterpreter','latex');
set(groot, 'defaultLegendInterpreter','latex');

NOTICE  - Initialization already done
WARNING - Detected verbosity = 4 in Publish mode ; not recommended ! switching to 2 instead

Chapter 1 : Generate a mesh and initial base flow

Parameters

U1Max= 3/4.; % to have same ratio of mean velocities as for Poiseuille case
U2Max=1.;    % set to 1
R1=0.5; distance=4.5; D2=1; Lpipe = 0.01;
Xmax = 100;
YMax = 20;
bctype = 0; % select 0 for constant and 1 for Poiseuille and 2 for Tanh
% Mesh generation
paramMESH = [R1 distance D2 Lpipe Xmax YMax];
ffmesh = SF_Mesh('Mesh_ConcentricJets_Pipes.edp','params',paramMESH,'cleanworkdir','yes');
figure;subplot(2,1,1);SF_Plot(ffmesh,'mesh','title','Initial mesh');
subplot(2,1,2);SF_Plot(ffmesh,'mesh','title','Initial mesh','xlim',[-2 2],'ylim',[0 2]);

% Generation of an initial solution
bf = SF_BaseFlow(ffmesh,'Re',1,'bctype',bctype,'U1',U1Max,'U2',U2Max,'solver','Newton_Axi.edp');


% Adapt
%bf = SF_Adapt(bf,'anisomax',3,'nbjacoby',3);
% plots
%figure; SF_Plot(bf,'ux','xlim',[-1 8],'ylim',[0 8]);
%Xpos = 1; Y=[0:0.01:1.5];
%uxline=SF_ExtractData(bf,'ux',Xpos,Y);
%figure; plot(uxline,Y);xlabel('Ux(r,1)');ylabel('r');title('axial velocity at location x=1');

WARNING -  Your program uses depreciated syntax 'Params' to pass parameters 
WARNING -  It is advised to switch to new method using 'Options', and modify your Freefem solvers to detect parameters using 'getARGV'  
WARNING -  Folder ./WORK_ArcLength_Constant/MESHBF not found : creating it !

loop with increasing Re

Increasing Reynolds in a structured manner

ReTab = [10,30,50,55,60,65];
for Re = ReTab
    bf = SF_BaseFlow(bf,'Re',Re);
    [bf] = SF_Adapt(bf,'anisomax',3,'nbjacoby',10,'Hmax',2);
%    [bf] = SF_Adapt(bf,'anisomax',3,'nbjacoby',10,'Hmax',5);
end

plot last BF after this stage

figure; SF_Plot(bf,'ux','xlim',[-1 8],'ylim',[0 8],'title',['Re = ',num2str(bf.Re),'; E = ',num2str(bf.Energy)] );
hold on;  SF_Plot(bf,'psi','contour','only','xlim',[-1 12],'ylim',[0 8],'Clevels',[ - 1:.1:-.1, 0:.01:.0625,.1,.2, .5:.5:10]);

figure;subplot(2,1,1);SF_Plot(bf.mesh,'mesh','title','Adapted mesh');
subplot(2,1,2);SF_Plot(bf.mesh,'mesh','title','Initial mesh','xlim',[-2 2],'ylim',[0 2]);

WARNING -  Error in SF_Plot : Field psi does not exist

Test Arclength

 bf = SF_BFContinue(bf,'step',0.001,'solver','ArcLengthContinuationAxi.edp');
% note that the first step is still backwards and I don't understand why !!!

Arclength continuation loop

Re = bf.Re;
ReMax = 80; ReMin = 25; % this is the termination of the loop. Remin is in case the curve does not loop back.
stepMax = 2;
step = stepMax;
%EnerList = []; betaList = []; ReList = []; // NOW USELESS IF USING DATABASE !

while ( bf.Re < ReMax && bf.Re > ReMin && step > 1e-3)
    bf=SF_BFContinue(bf,'step',step,'solver','ArcLengthContinuationAxi.edp');
    if(bf.iter < 0)
        disp("Not converged. Arc-length step reduced by a factor 2");
        step = 0.5*step;
        bf = SF_BFContinue(bf,'step',step,'solver','ArcLengthContinuationAxi.edp');
         if(bf.iter < 0)
            disp("Not converged. Reducing again by a factor 10");
            step = 0.1*step;
            bf = SF_BFContinue(bf,'step',step,'solver','ArcLengthContinuationAxi.edp');
            if bf.iter<0
                disp('Arclength continuation failed')
                break
            end
         end
    end
    step = min(1.4*step,stepMax); % raise the step for next iteration
    Re = bf.Re;
    figure(45);plot(Re,bf.beta,'*'); pause(0.1); hold on;
end

echo 2 0.76578 0.6431 | /PRODCOM/Singularity/freefem++/v4.9-20220413/bin/FreeFem++-mpi -nw -v 0 ArcLengthContinuationAxi.edp  -U1 0.75 -U2 1 -bctype 0 -Symmetry S : Signal 73
WARNING - SF_core_freefem: Error while using FreeFem++  ; file = ArcLengthContinuationAxi.edp ; error code = 201 :  Your Newton iteration did not converge
WARNING - SF_BFcontinue computation did not converge
Not converged. Arc-length step reduced by a factor 2
echo 1 0.76578 0.6431 | /PRODCOM/Singularity/freefem++/v4.9-20220413/bin/FreeFem++-mpi -nw -v 0 ArcLengthContinuationAxi.edp  -U1 0.75 -U2 1 -bctype 0 -Symmetry S : Signal 73
WARNING - SF_core_freefem: Error while using FreeFem++  ; file = ArcLengthContinuationAxi.edp ; error code = 201 :  Your Newton iteration did not converge
WARNING - SF_BFcontinue computation did not converge
Not converged. Reducing again by a factor 10
echo 0.2744 0.95272 0.30386 | /PRODCOM/Singularity/freefem++/v4.9-20220413/bin/FreeFem++-mpi -nw -v 0 ArcLengthContinuationAxi.edp  -U1 0.75 -U2 1 -bctype 0 -Symmetry S : Signal 73
WARNING - SF_core_freefem: Error while using FreeFem++  ; file = ArcLengthContinuationAxi.edp ; error code = 201 :  Your Newton iteration did not converge
WARNING - SF_BFcontinue computation did not converge
Not converged. Arc-length step reduced by a factor 2

Generating the summary of Data Base for postprocessing

sfs = SF_Status;

################################################################################
...  SUMMARY OF YOUR DATABASE FOLDER :    ./WORK_ArcLength_Constant/
#################################################################################
 
.... CONTENT OF DIRECTORY ./WORK_ArcLength_Constant/MESHES :
     (list of meshes previously created/adapted ; couples of .msh/.ff2m files )
 
Index | Name              | generation mode | Date                 | Nv      
1     | FFMESH_000001.msh | initial         | 22-mars-2023 16:43:51 | 702     
2     | FFMESH_000002.msh | adapted         | 22-mars-2023 16:44:03 | 2465    
3     | FFMESH_000003.msh | adapted         | 22-mars-2023 16:44:19 | 3204    
4     | FFMESH_000004.msh | adapted         | 22-mars-2023 16:44:40 | 4235    
5     | FFMESH_000005.msh | adapted         | 22-mars-2023 16:45:01 | 5113    
6     | FFMESH_000006.msh | adapted         | 22-mars-2023 16:45:25 | 5835    
7     | FFMESH_000007.msh | adapted         | 22-mars-2023 16:45:52 | 5845    
 
#################################################################################
#################################################################################
 
.... CONTENT OF DIRECTORY ./WORK_ArcLength_Constant/BASEFLOWS
     (couples of .txt/.ff2m files )
 
 Index | Name              | Type         | Date                 | Mesh file         | Re         | beta       | Energy    
 1     | FFDATA_000001.txt | BaseFlow     | 22-mars-2023 16:43:55 | FFMESH_000001.msh | 1          | 3.8124     | 3.8124    
 2     | FFDATA_000002.txt | BaseFlow     | 22-mars-2023 16:44:02 | FFMESH_000001.msh | 10         | 18.5917    | 18.5917   
 3     | FFDATA_000003.txt | BaseFlow     | 22-mars-2023 16:44:17 | FFMESH_000002.msh | 30         | 106.998    | 106.998   
 4     | FFDATA_000004.txt | BaseFlow     | 22-mars-2023 16:44:38 | FFMESH_000003.msh | 50         | 154.689    | 154.689   
 5     | FFDATA_000005.txt | BaseFlow     | 22-mars-2023 16:44:58 | FFMESH_000004.msh | 55         | 164.412    | 164.412   
 6     | FFDATA_000006.txt | BaseFlow     | 22-mars-2023 16:45:23 | FFMESH_000005.msh | 60         | 171.999    | 171.999   
 7     | FFDATA_000007.txt | BaseFlow     | 22-mars-2023 16:45:50 | FFMESH_000006.msh | 65         | 178.162    | 178.162   
 8     | FFDATA_000008.txt | BaseFlow     | 22-mars-2023 16:46:34 | FFMESH_000007.msh | 64.9474    | 178.205    | 178.205   
 9     | FFDATA_000009.txt | BaseFlow     | 22-mars-2023 16:46:59 | FFMESH_000007.msh | 66.2246    | 179.736    | 179.736   
 10    | FFDATA_000010.txt | BaseFlow     | 22-mars-2023 16:47:22 | FFMESH_000007.msh | 67.5156    | 181.255    | 181.255   
 11    | FFDATA_000011.txt | BaseFlow     | 22-mars-2023 16:47:51 | FFMESH_000007.msh | 68.8181    | 182.765    | 182.765   
 12    | FFDATA_000012.txt | BaseFlow     | 22-mars-2023 16:48:22 | FFMESH_000007.msh | 70.1266    | 184.268    | 184.268   
 13    | FFDATA_000013.txt | BaseFlow     | 22-mars-2023 16:48:54 | FFMESH_000007.msh | 71.4252    | 185.777    | 185.777   
 14    | FFDATA_000014.txt | BaseFlow     | 22-mars-2023 16:49:31 | FFMESH_000007.msh | 72.611     | 187.37     | 187.37    
 15    | FFDATA_000015.txt | BaseFlow     | 22-mars-2023 16:53:05 | FFMESH_000007.msh | 72.6548    | 187.46     | 187.46    
 16    | FFDATA_000016.txt | BaseFlow     | 22-mars-2023 16:53:35 | FFMESH_000007.msh | 72.7057    | 187.59     | 187.59    
 17    | FFDATA_000017.txt | BaseFlow     | 22-mars-2023 16:54:06 | FFMESH_000007.msh | 72.7358    | 187.785    | 187.785   
 18    | FFDATA_000018.txt | BaseFlow     | 22-mars-2023 16:56:13 | FFMESH_000007.msh | 72.6877    | 187.917    | 187.917   
 19    | FFDATA_000019.txt | BaseFlow     | 22-mars-2023 16:56:46 | FFMESH_000007.msh | 72.5046    | 188.014    | 188.014   
 20    | FFDATA_000020.txt | BaseFlow     | 22-mars-2023 16:57:14 | FFMESH_000007.msh | 72.2322    | 188.018    | 188.018   
 21    | FFDATA_000021.txt | BaseFlow     | 22-mars-2023 16:57:45 | FFMESH_000007.msh | 71.8608    | 187.946    | 187.946   
 22    | FFDATA_000022.txt | BaseFlow     | 22-mars-2023 16:58:13 | FFMESH_000007.msh | 71.3572    | 187.784    | 187.784   
 23    | FFDATA_000023.txt | BaseFlow     | 22-mars-2023 16:58:45 | FFMESH_000007.msh | 70.6723    | 187.502    | 187.502   
 24    | FFDATA_000024.txt | BaseFlow     | 22-mars-2023 16:59:16 | FFMESH_000007.msh | 69.7366    | 187.053    | 187.053   
 25    | FFDATA_000025.txt | BaseFlow     | 22-mars-2023 16:59:47 | FFMESH_000007.msh | 68.4518    | 186.371    | 186.371   
 26    | FFDATA_000026.txt | BaseFlow     | 22-mars-2023 17:00:22 | FFMESH_000007.msh | 66.6976    | 185.378    | 185.378   
 27    | FFDATA_000027.txt | BaseFlow     | 22-mars-2023 17:00:57 | FFMESH_000007.msh | 64.9565    | 184.362    | 184.362   
 28    | FFDATA_000028.txt | BaseFlow     | 22-mars-2023 17:01:30 | FFMESH_000007.msh | 63.219     | 183.338    | 183.338   
 29    | FFDATA_000029.txt | BaseFlow     | 22-mars-2023 17:01:59 | FFMESH_000007.msh | 61.4794    | 182.317    | 182.317   
 30    | FFDATA_000030.txt | BaseFlow     | 22-mars-2023 17:02:30 | FFMESH_000007.msh | 59.7317    | 181.307    | 181.307   
 31    | FFDATA_000031.txt | BaseFlow     | 22-mars-2023 17:03:05 | FFMESH_000007.msh | 57.9677    | 180.324    | 180.324   
 32    | FFDATA_000032.txt | BaseFlow     | 22-mars-2023 17:03:41 | FFMESH_000007.msh | 56.1765    | 179.388    | 179.388   
 33    | FFDATA_000033.txt | BaseFlow     | 22-mars-2023 17:04:16 | FFMESH_000007.msh | 54.3444    | 178.53     | 178.53    
 34    | FFDATA_000034.txt | BaseFlow     | 22-mars-2023 17:04:53 | FFMESH_000007.msh | 52.4563    | 177.798    | 177.798   
 35    | FFDATA_000035.txt | BaseFlow     | 22-mars-2023 17:05:30 | FFMESH_000007.msh | 50.5015    | 177.263    | 177.263   
 36    | FFDATA_000036.txt | BaseFlow     | 22-mars-2023 17:06:01 | FFMESH_000007.msh | 48.4907    | 177.026    | 177.026   
 37    | FFDATA_000037.txt | BaseFlow     | 22-mars-2023 17:06:30 | FFMESH_000007.msh | 46.4833    | 177.191    | 177.191   
 38    | FFDATA_000038.txt | BaseFlow     | 22-mars-2023 17:07:04 | FFMESH_000007.msh | 44.5859    | 177.798    | 177.798   
 39    | FFDATA_000039.txt | BaseFlow     | 22-mars-2023 17:07:46 | FFMESH_000007.msh | 42.8819    | 178.785    | 178.785   
 40    | FFDATA_000040.txt | BaseFlow     | 22-mars-2023 17:08:33 | FFMESH_000007.msh | 41.3858    | 180.043    | 180.043   
 41    | FFDATA_000041.txt | BaseFlow     | 22-mars-2023 17:09:20 | FFMESH_000007.msh | 40.0726    | 181.486    | 181.486   
 42    | FFDATA_000042.txt | BaseFlow     | 22-mars-2023 17:10:06 | FFMESH_000007.msh | 38.9096    | 183.052    | 183.052   
 43    | FFDATA_000043.txt | BaseFlow     | 22-mars-2023 17:10:51 | FFMESH_000007.msh | 37.8682    | 184.706    | 184.706   
 44    | FFDATA_000044.txt | BaseFlow     | 22-mars-2023 17:11:29 | FFMESH_000007.msh | 36.926     | 186.421    | 186.421   
 45    | FFDATA_000045.txt | BaseFlow     | 22-mars-2023 17:12:09 | FFMESH_000007.msh | 36.0655    | 188.182    | 188.182   
 46    | FFDATA_000046.txt | BaseFlow     | 22-mars-2023 17:12:51 | FFMESH_000007.msh | 35.2734    | 189.978    | 189.978   
 47    | FFDATA_000047.txt | BaseFlow     | 22-mars-2023 17:13:31 | FFMESH_000007.msh | 34.5394    | 191.802    | 191.802   
 48    | FFDATA_000048.txt | BaseFlow     | 22-mars-2023 17:14:13 | FFMESH_000007.msh | 33.8552    | 193.647    | 193.647   
 49    | FFDATA_000049.txt | BaseFlow     | 22-mars-2023 17:14:56 | FFMESH_000007.msh | 33.2144    | 195.51     | 195.51    
 50    | FFDATA_000050.txt | BaseFlow     | 22-mars-2023 17:15:35 | FFMESH_000007.msh | 32.6117    | 197.387    | 197.387   
 51    | FFDATA_000051.txt | BaseFlow     | 22-mars-2023 17:16:14 | FFMESH_000007.msh | 32.0426    | 199.277    | 199.277   
 52    | FFDATA_000052.txt | BaseFlow     | 22-mars-2023 17:16:52 | FFMESH_000007.msh | 31.5037    | 201.176    | 201.176   
 53    | FFDATA_000053.txt | BaseFlow     | 22-mars-2023 17:17:32 | FFMESH_000007.msh | 30.9919    | 203.085    | 203.085   
 54    | FFDATA_000054.txt | BaseFlow     | 22-mars-2023 17:18:14 | FFMESH_000007.msh | 30.5046    | 205.001    | 205.001   
 55    | FFDATA_000055.txt | BaseFlow     | 22-mars-2023 17:18:54 | FFMESH_000007.msh | 30.0397    | 206.924    | 206.924   
 56    | FFDATA_000056.txt | BaseFlow     | 22-mars-2023 17:19:31 | FFMESH_000007.msh | 29.5952    | 208.853    | 208.853   
 57    | FFDATA_000057.txt | BaseFlow     | 22-mars-2023 17:20:08 | FFMESH_000007.msh | 29.1696    | 210.786    | 210.786   
 58    | FFDATA_000058.txt | BaseFlow     | 22-mars-2023 17:20:41 | FFMESH_000007.msh | 28.7613    | 212.725    | 212.725   
 59    | FFDATA_000059.txt | BaseFlow     | 22-mars-2023 17:21:14 | FFMESH_000007.msh | 28.3691    | 214.667    | 214.667   
 60    | FFDATA_000060.txt | BaseFlow     | 22-mars-2023 17:21:49 | FFMESH_000007.msh | 27.992     | 216.613    | 216.613   
 61    | FFDATA_000061.txt | BaseFlow     | 22-mars-2023 17:22:26 | FFMESH_000007.msh | 27.6289    | 218.562    | 218.562   
 62    | FFDATA_000062.txt | BaseFlow     | 22-mars-2023 17:23:02 | FFMESH_000007.msh | 27.2789    | 220.515    | 220.515   
 63    | FFDATA_000063.txt | BaseFlow     | 22-mars-2023 17:23:38 | FFMESH_000007.msh | 26.9412    | 222.469    | 222.469   
 64    | FFDATA_000064.txt | BaseFlow     | 22-mars-2023 17:24:12 | FFMESH_000007.msh | 26.6151    | 224.427    | 224.427   
 65    | FFDATA_000065.txt | BaseFlow     | 22-mars-2023 17:24:47 | FFMESH_000007.msh | 26.2999    | 226.387    | 226.387   
 66    | FFDATA_000066.txt | BaseFlow     | 22-mars-2023 17:25:21 | FFMESH_000007.msh | 25.9951    | 228.348    | 228.348   
 67    | FFDATA_000067.txt | BaseFlow     | 22-mars-2023 17:25:55 | FFMESH_000007.msh | 25.7       | 230.312    | 230.312   
 68    | FFDATA_000068.txt | BaseFlow     | 22-mars-2023 17:26:26 | FFMESH_000007.msh | 25.4143    | 232.278    | 232.278   
 69    | FFDATA_000069.txt | BaseFlow     | 22-mars-2023 17:27:05 | FFMESH_000007.msh | 25.1373    | 234.245    | 234.245   
 70    | FFDATA_000070.txt | BaseFlow     | 22-mars-2023 17:27:43 | FFMESH_000007.msh | 24.8688    | 236.214    | 236.214   
 
#################################################################################
 
.... CONTENT OF DIRECTORY ./WORK_ArcLength_Constant/MESHBF
     (couples of .txt/.ff2m files )
 
 Index | Name              | Type         | Date                 | Mesh file         | Re         | beta       | Energy     | U1         | U2         | bctype    
 1     | FFDATA_000001.txt | BaseFlow     | 22-mars-2023 16:43:55 | FFMESH_000001.msh | 1          | 3.8124     | 3.8124     | 0.75       | 1          | 0         
 
#################################################################################
 
.... CONTENT OF DIRECTORY ./WORK_ArcLength_Constant/MISC
     (couples of .txt/.ff2m files )
   NB this directory may contain various secondary files produced by StabFem,
      such as flowfields projected after adaptation but not recomputed, adaptation masks, etc... 
 
 Index | Name              | Type         | Date                 | Mesh file         | Re         | beta       | Energy     | U1         | U2         | bctype    
 1     | FFDATA_000001.txt | BaseFlow     | 22-mars-2023 16:44:05 | FFMESH_000002.msh | 10         | 18.5917    | 18.5917    | 0.75       | 1          | 0         
 2     | FFDATA_000002.txt | BaseFlow     | 22-mars-2023 16:44:22 | FFMESH_000003.msh | 30         | 106.998    | 106.998    | 0.75       | 1          | 0         
 3     | FFDATA_000003.txt | BaseFlow     | 22-mars-2023 16:44:43 | FFMESH_000004.msh | 50         | 154.689    | 154.689    | 0.75       | 1          | 0         
 4     | FFDATA_000004.txt | BaseFlow     | 22-mars-2023 16:45:04 | FFMESH_000005.msh | 55         | 164.412    | 164.412    | 0.75       | 1          | 0         
 5     | FFDATA_000005.txt | BaseFlow     | 22-mars-2023 16:45:29 | FFMESH_000006.msh | 60         | 171.999    | 171.999    | 0.75       | 1          | 0         
 6     | FFDATA_000006.txt | BaseFlow     | 22-mars-2023 16:45:56 | FFMESH_000007.msh | 65         | 178.162    | 178.162    | 0.75       | 1          | 0         
 
 
#################################################################################

redraw figure from database

figure; plot([sfs.BASEFLOWS.Re],[sfs.BASEFLOWS.beta]);xlabel('Re'); ylabel('\beta');xlim([ReMin,ReMax]);

figure; plot([sfs.BASEFLOWS.Re],[sfs.BASEFLOWS.Energy]);xlabel('Re'); ylabel('E');xlim([ReMin,ReMax]);

Plot last Base flow

figure; SF_Plot(bf,'ux','xlim',[-1 8],'ylim',[0 8],'title',['Re = ',num2str(bf.Re),'; E = ',num2str(bf.Energy)] );
hold on;  SF_Plot(bf,'psi','contour','only','Clevels',[ - 1:.1:-.1, 0:.01:.0625,.1,.2, .5:.5:10],'xlim',[-1 12],'ylim',[0 8]);

% larger range
figure; SF_Plot(bf,'ux','xlim',[-1 8],'ylim',[0 8],'title',['Re = ',num2str(bf.Re),'; E = ',num2str(bf.Energy)] );
hold on;  SF_Plot(bf,'psi','contour','only','Clevels',[ - 1:.1:-.1, 0:.01:.0625,.1,.2, .5:.5:10],'xlim',[-1 100],'ylim',[0 20]);

Note: To improve runtime build MEX function fftri2gridfast() from fftri2gridfast.c
Note: To improve runtime build MEX function fftri2gridfast() from fftri2gridfast.c

compare with base flow for Re=30 from main branch

bf= SF_Load('BASEFLOWS',6);
figure; SF_Plot(bf,'ux','xlim',[-1 8],'ylim',[0 8],'title',['Re = ',num2str(bf.Re),'; E = ',num2str(bf.Energy)] );
hold on;  SF_Plot(bf,'psi','contour','only','Clevels',[ - 1:.1:-.1, 0:.01:.0625,.1,.2, .5:.5:10],'xlim',[-1 12],'ylim',[0 8]);

% larger range
figure; SF_Plot(bf,'ux','xlim',[-1 8],'ylim',[0 8],'title',['Re = ',num2str(bf.Re),'; E = ',num2str(bf.Energy)] );
hold on;  SF_Plot(bf,'psi','contour','only','Clevels',[ - 1:.1:-.1, 0:.01:.0625,.1,.2, .5:.5:10],'xlim',[-1 100],'ylim',[0 20]);


% [[PUBLISH]]
%
fclose(fopen('ArcLength_Constant.success','w+'));