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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 -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 ====== 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...//
