Helium: convergence of setState_ph and setState_ps - Githubissues

thorade / HelmholtzMedia

Modelica library for the calculation of fluid properties from a Helmholtz energy equation of state (EoS).

BSD 3-Clause "New" or "Revised" License

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Helium: convergence of setState_ph and setState_ps #4

Closed thorade closed 11 years ago

thorade commented 11 years ago

For Helium, the two functions setState_ph and setState_ph have converge problems in the super-critical liquid-like region and in the super-critical vapour-like region. Three possible solutions:

Better start values. For water there the IAPWS backward equations, similar equations could be set up for other fluids. But that means quite a lot of work. I could not find any other, more general approaches for guessing start values.
Use a iterative procedure other than Newton. For example, Broyden (2D Secant) or nested 1D Ridders/Bisection/Brent/Regula falsi.
Make Newton more stable using linesearching and backtracking,
as described by e.g. Numerical Recipes 3rd ed.
http://books.google.de/books?id=DyykEZo4fwUC&pg=PA477
or by Numerik für Ingenieure und Naturwissenschaftler, 2nd ed., Dahmen (2008)
http://books.google.de/books?id=zWenT-hxDxEC&pg=PA200

thorade commented 11 years ago

setState_ps also has convergence problems. Why does the "globally convergent Newton" algorithm not converge?

thorade commented 11 years ago

another iterative method that might be a promising candidate for this case is described by M. Nikkhah-Bahrami and R. Oftadeh http://dx.doi.org/10.1016/j.amc.2009.07.028 R. Oftadeh, M. Nikkhah-Bahrami, und A. Najafi http://dx.doi.org/10.1016/j.amc.2010.07.075

thorade commented 11 years ago

Applicability of equations of state for modeling helium systems: http://dx.doi.org/10.1016/j.cryogenics.2012.03.002

does not mention the un-published interim RefProp-Helmholtz-EoS by Ortiz-Vega, D.O., Hall, K.R., Arp, V.D., and Lemmon, E.W.

thorade commented 11 years ago

maybe the iteration variables should not be d and T, but log(d) and T (at least in the gas-like region); something like dvar = if d>d_crit then d else log(d); but one of the two has to be ±1 to make the change-over steady

thorade commented 11 years ago

Some more ideas:

Make sure to never enter the 2-phase region during iteration. Any state with T>T_crit or d>sat.liq.d or d<sat.vap.d is guaranteed to be single-phase.
1D iterations using hybrid Newton+bisection are guaranteed to converge when given an interval that brackets the root. So, can setState_pT or setState_pd or setState_Ts be used to calculate better start values? To find a smaller interval?

thorade commented 11 years ago

closing for now, if convergence problems do appear again it will be reopened