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====== continuefields ======

Quadratic extrapolation of FlowField u(mu) as function of parameter mu
====== options ======

<code>
  continuesoln :                                                                                                      
        (ALPHA VERSION!) continue invariant solution of plane Couette flow in Reynolds number                       

options : 
  -r        --restart                                              start from three previously computed solutions
  -eqb      --equilibrium                                          search for equilibrium or relative equilibrium (trav wave)                                                                                                                   
  -orb      --periodicorbit                                        search for periodic orbit or relative periodic orbit 
  -poinc    --poincare                                             (relative) periodic orbit search constrained to I-D=0 Poincare section                                                                                                       
  -xrel     --xrelative                                            search over x phase shift for relative orbit or eqb  
  -zrel     --zrelative                                            search over z phase shift for relative orbit or eqb  
  -contRe   --continueRe                                           continue solution in Reynolds number                 
  -contdPdx  --continuedPdx                                         continue solution in imposed pressure gradient      
  -contLx   --continueLx                                           continue solution in streamwise width Lx             
  -contLz   --continueLz                                           continue solution in spanwise width Lz               
  -contAsp  --continueAspect                                       continue solution in aspect ratio Lx/Lz              
  -contDiag  --continueDiagonal                                     continue solution along diagonal with const aspect ratio Lx/Lz                                                                                                              
  -contLtarg  --continueLtarget                                      continue solution towards a target Lx,Lz           
  -up       --upwards                                              for non-restart searches, search in dir of increasing free parameter                                                                                                         
  -Lxtarg   --LxTarget          <real>      default == 6.28319     aim for this value of Lx                             
  -Lztarg   --LzTarget          <real>      default == 3.14159     aim for this value of Lz                             
  -T        --maptime           <real>      default == 20          initial guess for orbit period or time of eqb/reqb map f^T(u)                                                                                                                
  -R        --Reynolds          <real>      default == 400         Reynolds number                                      
  -dPdx     --dPdx              <real>      default == 0           imposed mean pressure gradient                       
  -s0       --s0                <real>      default == 0           start value for arclength (arbitrary)                
  -ds       --ds                <real>      default == 0.0001      initial arclength increment for quadratic extrapolation                                                                                                                      
  -adt      --adjustDt                                             adjust dt between continuation steps to keep CFL in bounds                                                                                                                   
  -dsmin    --dsmin             <real>      default == 1e-08       minimum arclength increment (in normalized D,Re space)                                                                                                                       
  -dsmax    --dsmax             <real>      default == 0.05        maximum arclength increment (in normalized D,Re space)                                                                                                                       
  -errmin   --errmin            <real>      default == 1e-05       minimum error for extrapolated guesses               
  -errmax   --errmax            <real>      default == 0.0001      maximum error for extrapolated guesses   
  ...
  -o        --outdir            <string>    default == ./          output directory
  -log      --logfile           <string>    default == findsoln.logoutput log (filename or "stdout")
  -dg       --digits            <int>       default == 8           number of digits for ReD.asc
  <flowfield>      (trailing arg 1)                                initial guess for Newton search
</code>

====== usage ======


Suppose you have an equilibrium velocity field at three different Reynolds numbers 
and you want to extrapolate to a new Reynolds number. Let the fields be EQ1Re350.ff,
EQ1Re360.ff, EQ1Re370.ff at Re=350, 360, and 370. Then you can produce
a quadratic extrapolation to Re=380 by running

  continuefields -dv  350 EQ1Re350  360 EQ1Re360  370 EQ1Re370  380 EQ1Re380

The last two arguments are the desired parameter value and the output filename. Previous 
arguments are inputs in parameter, flowfield pairs. 

The -dv option assures that the output field is divergence-free. This is especially 
useful when the extrapolation changes the cellsize (Lx,Lz). For example, suppose 
you have three equilibrium fields with slightly different cell sizes, say EQ1Lz21.ff,
EQ1Lz22.ff, and EQ1Lz23.ff at Lz=2.1, 2.2, and 2.3. To produce a quadratic extrapolation
to Lz=2.4, you would run

  continuefields -dv  2.1 EQ1Lz21  2.2 EQ1Lz22  2.3 EQ1Lz23  2.4 EQ1Lz24

The continuefields utility is especially useful for continuation around bifurcations. 
For example, you're tracking an equilibrium solution in a D vs Re plot (dissipation vs 
Reynolds number), and you notice that as Re approaches a fixed value (say Re=220), D 
starts to shoot up very rapidly. You suspect that the continuation is approaching a 
saddle-node bifurcation and that your solution is on the lower branch, and you want 
to "turn the corner" and get the upper branch solution. Suppose you have EQ1Re222,
EQ1Re221, and EQ1Re220. Then run 

  fieldprops -e EQ1Re222
  fieldprops -e EQ1Re221
  fieldprops -e EQ1Re220

etc. to get the value of D for each field. Let the values be 2.56, 2.60, and 2.65 
respectively. Then //to be continued...//
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