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Saturation Adjustment Convergence Testing

Overview

The saturation adjustment procedure requires solving a non-linear equation to find the temperature that satisfies thermodynamic equilibrium conditions. This document describes the convergence testing framework used to validate the robustness of different numerical methods across the input parameter space.

Purpose

While the Tested Profiles section shows physically meaningful thermodynamic states, this section explores convergence behavior across a broader parameter space. We test all permutations of inputs within given ranges of density ($\rho$), internal energy ($e_{int}$), and total specific humidity ($q_t$), including combinations that may not be physically meaningful but help identify the boundaries where convergence fails.

This testing framework is dedicated to monitoring and improving the performance and robustness of various numerical methods in solving saturation adjustment equations.

Performance Note

The dims parameter in docs/src/saturation_adjustment.jl is currently set to dims = (6, 6, 6) to avoid heavy computations during documentation builds. For higher resolution testing, increase it to dims = (10, 10, 10) or higher when running locally.

Convergence Maps

3D Parameter Space

The following maps show convergence behavior across the full 3D parameter space:

Numerical MethodConverged CasesNon-converged Cases
SecantMethod
NewtonsMethod

2D Slices by Total Specific Humidity

These maps show convergence behavior in 2D slices, binned by total specific humidity:

Numerical MethodConverged CasesNon-converged Cases
SecantMethod
NewtonsMethod

Implementation

The convergence testing is implemented in the following code:

include("saturation_adjustment.jl")
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=-84833.10860685963, q_tot=0.03380557431214914, T=239.75547239135682, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=-84833.10860685963, q_tot=0.03380557431214914, T=239.75547239135682, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=276.75511189930506, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=276.75511189930506, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=384.54126099898724, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=384.54126099898724, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=235788.0233316272, q_tot=0.1690278715607457, T=152.4769525993966, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=235788.0233316272, q_tot=0.1690278715607457, T=152.4769525993966, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=-57061.21364609245, q_tot=0.03380557431214914, T=253.03613162544377, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=-57061.21364609245, q_tot=0.03380557431214914, T=253.03613162544377, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=-57061.21364609245, q_tot=0.03380557431214914, T=307.1444746935539, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=-57061.21364609245, q_tot=0.03380557431214914, T=307.1444746935539, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=23956.18108875872, q_tot=0.06761114862429828, T=418.4218300820586, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=23956.18108875872, q_tot=0.06761114862429828, T=418.4218300820586, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=104973.57582360992, q_tot=0.10141672293644742, T=261.43085310333174, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=104973.57582360992, q_tot=0.10141672293644742, T=261.43085310333174, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=185990.97055846106, q_tot=0.13522229724859655, T=265.9417799874928, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=185990.97055846106, q_tot=0.13522229724859655, T=265.9417799874928, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=267008.3652933123, q_tot=0.1690278715607457, T=268.6340429214656, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=267008.3652933123, q_tot=0.1690278715607457, T=268.6340429214656, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=276.38835095874884, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=276.38835095874884, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=52590.18779975541, q_tot=0.06761114862429828, T=258.13252013749593, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=52590.18779975541, q_tot=0.06761114862429828, T=258.13252013749593, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=52590.18779975541, q_tot=0.06761114862429828, T=339.80370134938573, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=52590.18779975541, q_tot=0.06761114862429828, T=339.80370134938573, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=134469.69428483612, q_tot=0.10141672293644742, T=265.02238708736604, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=134469.69428483612, q_tot=0.10141672293644742, T=265.02238708736604, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=134469.69428483612, q_tot=0.10141672293644742, T=394.54848555323406, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.026051592999156627, e_int=134469.69428483612, q_tot=0.10141672293644742, T=394.54848555323406, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=216349.20076991676, q_tot=0.13522229724859655, T=275.9113417489861, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=216349.20076991676, q_tot=0.13522229724859655, T=275.9113417489861, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=298228.7072549974, q_tot=0.1690278715607457, T=286.0135663425113, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=298228.7072549974, q_tot=0.1690278715607457, T=286.0135663425113, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=246707.4309813724, q_tot=0.13522229724859655, T=270.8804064498306, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=246707.4309813724, q_tot=0.13522229724859655, T=270.8804064498306, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=329449.04921668256, q_tot=0.1690278715607457, T=272.3740141507237, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.026051592999156627, e_int=329449.04921668256, q_tot=0.1690278715607457, T=272.3740141507237, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=378.00231383432094, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=378.00231383432094, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=75477.45736238381, q_tot=0.10141672293644742, T=317.98853108610234, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=75477.45736238381, q_tot=0.10141672293644742, T=317.98853108610234, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=75477.45736238381, q_tot=0.10141672293644742, T=480.3794718092198, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=75477.45736238381, q_tot=0.10141672293644742, T=480.3794718092198, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=155632.7403470055, q_tot=0.13522229724859655, T=295.2294227147173, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=155632.7403470055, q_tot=0.13522229724859655, T=295.2294227147173, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=155632.7403470055, q_tot=0.13522229724859655, T=568.271108352621, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=155632.7403470055, q_tot=0.13522229724859655, T=568.271108352621, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=235788.0233316272, q_tot=0.1690278715607457, T=646.8398310411774, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=235788.0233316272, q_tot=0.1690278715607457, T=646.8398310411774, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=-57061.21364609245, q_tot=0.03380557431214914, T=264.6693026110088, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=-57061.21364609245, q_tot=0.03380557431214914, T=264.6693026110088, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=23956.18108875872, q_tot=0.06761114862429828, T=416.87639488506073, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=23956.18108875872, q_tot=0.06761114862429828, T=416.87639488506073, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=104973.57582360992, q_tot=0.10141672293644742, T=515.0766660000132, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=104973.57582360992, q_tot=0.10141672293644742, T=515.0766660000132, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=185990.97055846106, q_tot=0.13522229724859655, T=293.7774758738947, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=185990.97055846106, q_tot=0.13522229724859655, T=293.7774758738947, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=185990.97055846106, q_tot=0.13522229724859655, T=601.6593389556886, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=185990.97055846106, q_tot=0.13522229724859655, T=601.6593389556886, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=267008.3652933123, q_tot=0.1690278715607457, T=301.88350156442874, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=267008.3652933123, q_tot=0.1690278715607457, T=301.88350156442874, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=267008.3652933123, q_tot=0.1690278715607457, T=679.243432288671, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=267008.3652933123, q_tot=0.1690278715607457, T=679.243432288671, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=321.202869738184, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=321.202869738184, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=52590.18779975541, q_tot=0.06761114862429828, T=430.4297731554195, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=52590.18779975541, q_tot=0.06761114862429828, T=430.4297731554195, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=134469.69428483612, q_tot=0.10141672293644742, T=293.6168323043758, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=134469.69428483612, q_tot=0.10141672293644742, T=293.6168323043758, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=134469.69428483612, q_tot=0.10141672293644742, T=519.3845179926648, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=134469.69428483612, q_tot=0.10141672293644742, T=519.3845179926648, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=216349.20076991676, q_tot=0.13522229724859655, T=299.59338360538777, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=216349.20076991676, q_tot=0.13522229724859655, T=299.59338360538777, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=216349.20076991676, q_tot=0.13522229724859655, T=599.065556739206, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=216349.20076991676, q_tot=0.13522229724859655, T=599.065556739206, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=298228.7072549974, q_tot=0.1690278715607457, T=297.7899642078078, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=298228.7072549974, q_tot=0.1690278715607457, T=297.7899642078078, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=298228.7072549974, q_tot=0.1690278715607457, T=671.1942841672223, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=298228.7072549974, q_tot=0.1690278715607457, T=671.1942841672223, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=81224.19451075212, q_tot=0.06761114862429828, T=289.1755580184125, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=81224.19451075212, q_tot=0.06761114862429828, T=289.1755580184125, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=163965.8127460623, q_tot=0.10141672293644742, T=308.8963571676698, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=163965.8127460623, q_tot=0.10141672293644742, T=308.8963571676698, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=246707.4309813724, q_tot=0.13522229724859655, T=326.2047811545544, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=246707.4309813724, q_tot=0.13522229724859655, T=326.2047811545544, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=329449.04921668256, q_tot=0.1690278715607457, T=305.95573102003715, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=329449.04921668256, q_tot=0.1690278715607457, T=305.95573102003715, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=329449.04921668256, q_tot=0.1690278715607457, T=339.9874784187163, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.2285152841867505, e_int=329449.04921668256, q_tot=0.1690278715607457, T=339.9874784187163, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=277065.661192828, q_tot=0.13522229724859655, T=304.76138046749224, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=277065.661192828, q_tot=0.13522229724859655, T=304.76138046749224, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=360669.3911783676, q_tot=0.1690278715607457, T=308.6716171865542, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.2285152841867505, e_int=360669.3911783676, q_tot=0.1690278715607457, T=308.6716171865542, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=370.7079421435795, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=370.7079421435795, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=75477.45736238381, q_tot=0.10141672293644742, T=319.4924528237559, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=75477.45736238381, q_tot=0.10141672293644742, T=319.4924528237559, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=75477.45736238381, q_tot=0.10141672293644742, T=478.2671578138983, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=75477.45736238381, q_tot=0.10141672293644742, T=478.2671578138983, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=155632.7403470055, q_tot=0.13522229724859655, T=566.6777294681642, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=155632.7403470055, q_tot=0.13522229724859655, T=566.6777294681642, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=235788.0233316272, q_tot=0.1690278715607457, T=645.0946798452474, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=235788.0233316272, q_tot=0.1690278715607457, T=645.0946798452474, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=23956.18108875872, q_tot=0.06761114862429828, T=290.6456935935173, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=23956.18108875872, q_tot=0.06761114862429828, T=290.6456935935173, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=23956.18108875872, q_tot=0.06761114862429828, T=413.71641541745913, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=23956.18108875872, q_tot=0.06761114862429828, T=413.71641541745913, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=104973.57582360992, q_tot=0.10141672293644742, T=513.6322192766334, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=104973.57582360992, q_tot=0.10141672293644742, T=513.6322192766334, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=185990.97055846106, q_tot=0.13522229724859655, T=600.3614102483324, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=185990.97055846106, q_tot=0.13522229724859655, T=600.3614102483324, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=267008.3652933123, q_tot=0.1690278715607457, T=189.98156207951757, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=267008.3652933123, q_tot=0.1690278715607457, T=189.98156207951757, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=267008.3652933123, q_tot=0.1690278715607457, T=677.6354027730646, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=267008.3652933123, q_tot=0.1690278715607457, T=677.6354027730646, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=315.5227540914897, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=315.5227540914897, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=52590.18779975541, q_tot=0.06761114862429828, T=438.753578777839, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=52590.18779975541, q_tot=0.06761114862429828, T=438.753578777839, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=134469.69428483612, q_tot=0.10141672293644742, T=531.745669081948, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=134469.69428483612, q_tot=0.10141672293644742, T=531.745669081948, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=216349.20076991676, q_tot=0.13522229724859655, T=614.0689897956252, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=216349.20076991676, q_tot=0.13522229724859655, T=614.0689897956252, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=298228.7072549974, q_tot=0.1690278715607457, T=315.9246671900151, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=298228.7072549974, q_tot=0.1690278715607457, T=315.9246671900151, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=298228.7072549974, q_tot=0.1690278715607457, T=687.923060453338, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=298228.7072549974, q_tot=0.1690278715607457, T=687.923060453338, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=81224.19451075212, q_tot=0.06761114862429828, T=300.73891333424046, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=81224.19451075212, q_tot=0.06761114862429828, T=300.73891333424046, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=163965.8127460623, q_tot=0.10141672293644742, T=329.10328879844116, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=163965.8127460623, q_tot=0.10141672293644742, T=329.10328879844116, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=246707.4309813724, q_tot=0.13522229724859655, T=313.1109813881466, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=246707.4309813724, q_tot=0.13522229724859655, T=313.1109813881466, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=246707.4309813724, q_tot=0.13522229724859655, T=348.6580019088974, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=246707.4309813724, q_tot=0.13522229724859655, T=348.6580019088974, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=329449.04921668256, q_tot=0.1690278715607457, T=317.9228115154708, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.4309789753743443, e_int=329449.04921668256, q_tot=0.1690278715607457, T=317.9228115154708, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=329449.04921668256, q_tot=0.1690278715607457, T=363.2020036862111, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=329449.04921668256, q_tot=0.1690278715607457, T=363.2020036862111, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=360669.3911783676, q_tot=0.1690278715607457, T=319.6887955591078, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.4309789753743443, e_int=360669.3911783676, q_tot=0.1690278715607457, T=319.6887955591078, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=362.40849594714916, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=362.40849594714916, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.6334426665619382, e_int=75477.45736238381, q_tot=0.10141672293644742, T=319.57324884367824, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.6334426665619382, e_int=75477.45736238381, q_tot=0.10141672293644742, T=319.57324884367824, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=75477.45736238381, q_tot=0.10141672293644742, T=476.13098539164247, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=75477.45736238381, q_tot=0.10141672293644742, T=476.13098539164247, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.6334426665619382, e_int=155632.7403470055, q_tot=0.13522229724859655, T=312.5393244697833, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.6334426665619382, e_int=155632.7403470055, q_tot=0.13522229724859655, T=312.5393244697833, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=155632.7403470055, q_tot=0.13522229724859655, T=565.0834349801744, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=155632.7403470055, q_tot=0.13522229724859655, T=565.0834349801744, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=235788.0233316272, q_tot=0.1690278715607457, T=643.3570796361968, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=235788.0233316272, q_tot=0.1690278715607457, T=643.3570796361968, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=23956.18108875872, q_tot=0.06761114862429828, T=410.37965388696756, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=23956.18108875872, q_tot=0.06761114862429828, T=410.37965388696756, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=104973.57582360992, q_tot=0.10141672293644742, T=512.0979348962413, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=104973.57582360992, q_tot=0.10141672293644742, T=512.0979348962413, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=185990.97055846106, q_tot=0.13522229724859655, T=598.9665839713971, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=185990.97055846106, q_tot=0.13522229724859655, T=598.9665839713971, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.6334426665619382, e_int=267008.3652933123, q_tot=0.1690278715607457, T=321.4258887125516, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.6334426665619382, e_int=267008.3652933123, q_tot=0.1690278715607457, T=321.4258887125516, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=267008.3652933123, q_tot=0.1690278715607457, T=675.9266539270102, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=267008.3652933123, q_tot=0.1690278715607457, T=675.9266539270102, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=302.703924003142, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=302.703924003142, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=52590.18779975541, q_tot=0.06761114862429828, T=440.7615910559167, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=52590.18779975541, q_tot=0.06761114862429828, T=440.7615910559167, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=134469.69428483612, q_tot=0.10141672293644742, T=535.6871118537781, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=134469.69428483612, q_tot=0.10141672293644742, T=535.6871118537781, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.6334426665619382, e_int=216349.20076991676, q_tot=0.13522229724859655, T=251.67105181319369, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.6334426665619382, e_int=216349.20076991676, q_tot=0.13522229724859655, T=251.67105181319369, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=216349.20076991676, q_tot=0.13522229724859655, T=618.942203801297, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=216349.20076991676, q_tot=0.13522229724859655, T=618.942203801297, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=298228.7072549974, q_tot=0.1690278715607457, T=693.1416008257517, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=298228.7072549974, q_tot=0.1690278715607457, T=693.1416008257517, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=81224.19451075212, q_tot=0.06761114862429828, T=307.2232997921579, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=81224.19451075212, q_tot=0.06761114862429828, T=307.2232997921579, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=163965.8127460623, q_tot=0.10141672293644742, T=338.6912887011851, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=163965.8127460623, q_tot=0.10141672293644742, T=338.6912887011851, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.6334426665619382, e_int=246707.4309813724, q_tot=0.13522229724859655, T=320.52204348449214, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.6334426665619382, e_int=246707.4309813724, q_tot=0.13522229724859655, T=320.52204348449214, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=246707.4309813724, q_tot=0.13522229724859655, T=358.99149311892234, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=246707.4309813724, q_tot=0.13522229724859655, T=358.99149311892234, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=329449.04921668256, q_tot=0.1690278715607457, T=373.5719836954814, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=329449.04921668256, q_tot=0.1690278715607457, T=373.5719836954814, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=277065.661192828, q_tot=0.13522229724859655, T=322.75980196686976, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=277065.661192828, q_tot=0.13522229724859655, T=322.75980196686976, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=360669.3911783676, q_tot=0.1690278715607457, T=331.9931883788953, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.6334426665619382, e_int=360669.3911783676, q_tot=0.1690278715607457, T=331.9931883788953, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=352.7050750556498, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=352.7050750556498, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.835906357749532, e_int=75477.45736238381, q_tot=0.10141672293644742, T=305.0178688950608, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.835906357749532, e_int=75477.45736238381, q_tot=0.10141672293644742, T=305.0178688950608, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=75477.45736238381, q_tot=0.10141672293644742, T=473.9698231000046, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=75477.45736238381, q_tot=0.10141672293644742, T=473.9698231000046, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.835906357749532, e_int=155632.7403470055, q_tot=0.13522229724859655, T=317.47505470917264, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.835906357749532, e_int=155632.7403470055, q_tot=0.13522229724859655, T=317.47505470917264, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=155632.7403470055, q_tot=0.13522229724859655, T=563.488108797756, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=155632.7403470055, q_tot=0.13522229724859655, T=563.488108797756, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=235788.0233316272, q_tot=0.1690278715607457, T=641.6268662278559, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=235788.0233316272, q_tot=0.1690278715607457, T=641.6268662278559, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=23956.18108875872, q_tot=0.06761114862429828, T=406.8998256046614, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=23956.18108875872, q_tot=0.06761114862429828, T=406.8998256046614, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=104973.57582360992, q_tot=0.10141672293644742, T=510.5340724048241, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=104973.57582360992, q_tot=0.10141672293644742, T=510.5340724048241, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=185990.97055846106, q_tot=0.13522229724859655, T=597.5470425902379, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=185990.97055846106, q_tot=0.13522229724859655, T=597.5470425902379, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=267008.3652933123, q_tot=0.1690278715607457, T=674.198423754555, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=267008.3652933123, q_tot=0.1690278715607457, T=674.198423754555, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=288.71455630887414, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=288.71455630887414, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=52590.18779975541, q_tot=0.06761114862429828, T=440.8961130944243, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=52590.18779975541, q_tot=0.06761114862429828, T=440.8961130944243, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=134469.69428483612, q_tot=0.10141672293644742, T=537.1614790818081, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=134469.69428483612, q_tot=0.10141672293644742, T=537.1614790818081, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=216349.20076991676, q_tot=0.13522229724859655, T=620.861107495042, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=216349.20076991676, q_tot=0.13522229724859655, T=620.861107495042, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.835906357749532, e_int=298228.7072549974, q_tot=0.1690278715607457, T=327.8791904369133, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.835906357749532, e_int=298228.7072549974, q_tot=0.1690278715607457, T=327.8791904369133, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=298228.7072549974, q_tot=0.1690278715607457, T=695.020421511467, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=298228.7072549974, q_tot=0.1690278715607457, T=695.020421511467, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=81224.19451075212, q_tot=0.06761114862429828, T=310.4659425437634, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=81224.19451075212, q_tot=0.06761114862429828, T=310.4659425437634, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=163965.8127460623, q_tot=0.10141672293644742, T=343.3914900781351, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=163965.8127460623, q_tot=0.10141672293644742, T=343.3914900781351, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=246707.4309813724, q_tot=0.13522229724859655, T=364.19604625405407, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=246707.4309813724, q_tot=0.13522229724859655, T=364.19604625405407, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.835906357749532, e_int=329449.04921668256, q_tot=0.1690278715607457, T=331.4282713813616, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=0.835906357749532, e_int=329449.04921668256, q_tot=0.1690278715607457, T=331.4282713813616, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=329449.04921668256, q_tot=0.1690278715607457, T=378.77030098024153, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=329449.04921668256, q_tot=0.1690278715607457, T=378.77030098024153, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=277065.661192828, q_tot=0.13522229724859655, T=330.52032150030124, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=277065.661192828, q_tot=0.13522229724859655, T=330.52032150030124, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=360669.3911783676, q_tot=0.1690278715607457, T=344.34293493481493, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=0.835906357749532, e_int=360669.3911783676, q_tot=0.1690278715607457, T=344.34293493481493, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=340.91061352576673, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=-4677.825622237928, q_tot=0.06761114862429828, T=340.91061352576673, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=75477.45736238381, q_tot=0.10141672293644742, T=471.782433862329, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=75477.45736238381, q_tot=0.10141672293644742, T=471.782433862329, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=1.038370048937126, e_int=155632.7403470055, q_tot=0.13522229724859655, T=320.1609121571234, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=1.038370048937126, e_int=155632.7403470055, q_tot=0.13522229724859655, T=320.1609121571234, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=155632.7403470055, q_tot=0.13522229724859655, T=561.8915963727093, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=155632.7403470055, q_tot=0.13522229724859655, T=561.8915963727093, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=235788.0233316272, q_tot=0.1690278715607457, T=639.9038384261646, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=235788.0233316272, q_tot=0.1690278715607457, T=639.9038384261646, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=23956.18108875872, q_tot=0.06761114862429828, T=403.273325406335, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=23956.18108875872, q_tot=0.06761114862429828, T=403.273325406335, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=104973.57582360992, q_tot=0.10141672293644742, T=508.9536961521723, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=104973.57582360992, q_tot=0.10141672293644742, T=508.9536961521723, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=185990.97055846106, q_tot=0.13522229724859655, T=596.1185954042426, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=185990.97055846106, q_tot=0.13522229724859655, T=596.1185954042426, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=267008.3652933123, q_tot=0.1690278715607457, T=672.4683844859339, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=267008.3652933123, q_tot=0.1690278715607457, T=672.4683844859339, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=290.09997720901333, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=-29289.31868532524, q_tot=0.03380557431214914, T=290.09997720901333, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=52590.18779975541, q_tot=0.06761114862429828, T=440.2133873721683, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=52590.18779975541, q_tot=0.06761114862429828, T=440.2133873721683, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=134469.69428483612, q_tot=0.10141672293644742, T=537.5798279899681, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=134469.69428483612, q_tot=0.10141672293644742, T=537.5798279899681, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=216349.20076991676, q_tot=0.13522229724859655, T=621.5207502117654, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=216349.20076991676, q_tot=0.13522229724859655, T=621.5207502117654, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=1.038370048937126, e_int=298228.7072549974, q_tot=0.1690278715607457, T=285.3307472617114, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=1.038370048937126, e_int=298228.7072549974, q_tot=0.1690278715607457, T=285.3307472617114, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=298228.7072549974, q_tot=0.1690278715607457, T=695.4833344576799, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=298228.7072549974, q_tot=0.1690278715607457, T=695.4833344576799, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=81224.19451075212, q_tot=0.06761114862429828, T=313.97904230585135, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=81224.19451075212, q_tot=0.06761114862429828, T=313.97904230585135, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=163965.8127460623, q_tot=0.10141672293644742, T=345.4338166112704, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=163965.8127460623, q_tot=0.10141672293644742, T=345.4338166112704, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=246707.4309813724, q_tot=0.13522229724859655, T=366.7371050567311, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=246707.4309813724, q_tot=0.13522229724859655, T=366.7371050567311, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=329449.04921668256, q_tot=0.1690278715607457, T=381.35715814645187, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=329449.04921668256, q_tot=0.1690278715607457, T=381.35715814645187, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=277065.661192828, q_tot=0.13522229724859655, T=339.18544677041587, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=277065.661192828, q_tot=0.13522229724859655, T=339.18544677041587, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=360669.3911783676, q_tot=0.1690278715607457, T=355.957175987886, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
NewtonsMethod(ρ=1.038370048937126, e_int=360669.3911783676, q_tot=0.1690278715607457, T=355.957175987886, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=1.038370048937126, e_int=391889.73314005276, q_tot=0.1690278715607457, T=341.10704534450747, maxiter=10, tol=0.0001)
maxiter reached in saturation_adjustment(ρeq):
SecantMethod(ρ=1.038370048937126, e_int=391889.73314005276, q_tot=0.1690278715607457, T=341.10704534450747, maxiter=10, tol=0.0001)
Convergence percentages:
RootSolvers.NewtonsMethod = 0.5370370370370371
RootSolvers.SecantMethod = 0.8148148148148148

Interpretation

  • Converged regions (green/blue areas) indicate parameter combinations where the numerical method successfully finds a solution
  • Non-converged regions (red areas) indicate parameter combinations where the method fails to converge
  • Boundary regions help identify the robustness limits of each numerical method
  • Physical relevance should be considered when interpreting results - some non-converged regions may correspond to unphysical parameter combinations

Numerical Methods Tested

  1. SecantMethod: A derivative-free method that uses finite differences to approximate derivatives
  2. NewtonsMethod: Uses analytical derivatives for potentially faster convergence

Usage Guidelines

  • Use these maps to understand the convergence characteristics of different numerical methods
  • Consider the trade-offs between robustness (SecantMethod) and efficiency (NewtonsMethod)
  • The tested parameter ranges should cover your expected simulation conditions
  • For production use, ensure your parameter combinations fall within well-converged regions