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

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

====== options ======

  -dv       --divergence                                           project field onto div-free subspace
  -e        --epsilon           <real>      default == 1e-13       don't interpolate Lx,Lz,a,b if |diffs| < eps
  mu1              (trailing arg 8)                                parameter for u1
  <flowfield>      (trailing arg 7)                                input field u1
  mu2              (trailing arg 6)                                parameter for u2
  <flowfield>      (trailing arg 5)                                input field u2
  mu3              (trailing arg 4)                                parameter for u3
  <flowfield>      (trailing arg 3)                                input field u3
  mu               (trailing arg 2)                                parameter for output field
  <flowfield>      (trailing arg 1)                                output field
====== 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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