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

Quadratic extrapolation of FlowField u(mu) as function of parameter mu, where mu is one of Reynolds number, //dP/dx, Lx, Lz, Lx/Lz, sqrt(Lx^2 + Lz^2),// or the length between the starting //(Lx,Lz)// and a target value of //(Lx,Lz)//.

====== 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  
  -sigma    --sigma             <string>                           file containing sigma of sigma f^T(u) - u = 0 (default == identity)                                                                                                          
  -symms    --symmetries        <string>                           file containing generators of isotropy group for symmetry-constrained search                                                                                                 
  ...
  -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 ======
===== start-up mode =====

There are two basic modes for starting a continuation: from scratch (a single previous solution), or from a previous continuation (using three successive steps). Starting from scratch looks like this

  continuesoln -eqb -contRe -R 350 uRe350.h5
  
The trailing argument here is a FlowField which is assumed to be a solution of the specified type at the specified parameters (or a good guess for a solution). The continuation will begin by making very small +/- perturbations in the continuation parameter (here Reynolds number) and finding new solutions at that value using the input field as an initial guess. By default the continuation goes down in the parameter. If you want to go up, use the ''-up'' option. 

Starting from a previous continuation looks like this

  continuesoln -eqb -contRe --restart   ../contRe0/search-14 ../contRe0/search-15 ../contRe0/search-16

The trailing three arguments are directories containing results from a previous run of ''continuesoln''. The direction of continuation is determined by the order of the three previous solutions. 
===== continuation parameter =====

''continuesoln'' will continue solutions in one of seven parameters:
   
   -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 in Lx,Lz with const aspect ratio Lx/Lz                                                                                                              
   -contLtarg --continueLtarget              continue solution towards a specified Lx,Lz pair 

The target //Lx,Lz// for ''-contLtarg'' is specified by these options

   -Lxtarg   --LxTarget          <real>      default == 6.28319     aim for this value of Lx                             
   -Lztarg   --LzTarget          <real>      default == 3.14159     aim for this value of Lz 

Two other options related to the continuation type are 

   -up       --upwards                       continue upwards in parameter (default is downwards)
   -adt      --adjustDt                      adjust dt between continuation steps to keep CFL in bounds 
  
The ''-up'' option is self-explanatory. The ''-adt'' option is most important when the continuation changes //Lx//, since this will change the //x// gridspacing and consequently the CFL number. It should be safe to use ''-adt'' in other cases, too.
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