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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//
