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--- | ||
title: Nelson Work-Precision Diagrams | ||
author: Stella Offner and Chris Rackauckas | ||
--- | ||
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```julia | ||
using OrdinaryDiffEq | ||
using Plots | ||
using Sundials | ||
using ODEInterface, ODEInterfaceDiffEq | ||
``` | ||
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```julia | ||
T = 10 | ||
Av = 2 # This is what depotic uses for visual extinction | ||
Go = 1.7 # I think despotic uses 1.7 | ||
n_H = 611 | ||
shield = 1 | ||
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function Nelson_ODE(du,u,p,t) | ||
# 1: H2 | ||
#= du[1] = -1.2e-17 * u[1] + | ||
n_H * (1.9e-6 * u[2] * u[3]) / (T^0.54) - | ||
n_H * 4e-16 * u[1] * u[12] - | ||
n_H * 7e-15 * u[1] * u[5] + | ||
n_H * 1.7e-9 * u[10] * u[2] + | ||
n_H * 2e-9 * u[2] * u[6] + | ||
n_H * 2e-9 * u[2] * u[14] + | ||
n_H * 8e-10 * u[2] * u[8] =# | ||
du[1] = 0 | ||
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# 2: H3+ | ||
du[2] = 1.2e-17 * u[1] + | ||
n_H * (-1.9e-6 * u[3] * u[2]) / (T^0.54) - | ||
n_H * 1.7e-9 * u[10] * u[2] - | ||
n_H * 2e-9 * u[2] * u[6] - | ||
n_H * 2e-9 * u[2] * u[14] - | ||
n_H * 8e-10 * u[2] * u[8] | ||
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# 3: e | ||
du[3] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - | ||
n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - | ||
n_H * (3.3e-5 * u[11] * u[3]) / T + | ||
1.2e-17 * u[1] - | ||
n_H * (1.9e-6 * u[3] * u[2]) / (T^0.54) + | ||
6.8e-18 * u[4] - | ||
n_H * (9e-11 * u[3] * u[5]) / (T^0.64) + | ||
3e-10 * Go * exp(-3 * Av) * u[6] + | ||
n_H * 2e-9 * u[2] * u[13] ## CHECK I added this extra term from a CR ionization reaction | ||
+ 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction | ||
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# 4: He | ||
du[4] = n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - | ||
6.8e-18 * u[4] + | ||
n_H * 7e-15 * u[1] * u[5] + | ||
n_H * 1.6e-9 * u[10] * u[5] | ||
#du[4] = 0 | ||
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# 5: He+ 6.8e-18 or 1.1 | ||
du[5] = 6.8e-18 * u[4] - | ||
n_H * (9e-11 * u[3] * u[5]) / (T^0.64) - | ||
n_H * 7e-15 * u[1] * u[5] - | ||
n_H * 1.6e-9 * u[10] * u[5] | ||
#u[5] = 0 | ||
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# 6: C | ||
du[6] = n_H * (1.4e-10 * u[3] * u[12]) / (T^0.61) - | ||
n_H * 2e-9 * u[2] * u[6] - | ||
n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] + | ||
1e-9 * Go * exp(-1.5 * Av) * u[7] - | ||
3e-10 * Go * exp(-3 * Av) * u[6] + | ||
1e-10 * Go * exp(-3 * Av) * u[10] * shield | ||
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# 7: CHx | ||
du[7] = n_H * (-2e-10) * u[7] * u[8] + | ||
n_H * 4e-16 * u[1] * u[12] + | ||
n_H * 2e-9 * u[2] * u[6] - | ||
1e-9 * Go * u[7] * exp(-1.5 * Av) | ||
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# 8: O | ||
du[8] = n_H * (-2e-10) * u[7] * u[8] + | ||
n_H * 1.6e-9 * u[10] * u[5] - | ||
n_H * 8e-10 * u[2] * u[8] + | ||
5e-10 * Go * exp(-1.7 * Av) * u[9] + | ||
1e-10 * Go * exp(-3 * Av) * u[10] * shield | ||
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# 9: OHx | ||
du[9] = n_H * (-1e-9) * u[9] * u[12] + | ||
n_H * 8e-10 * u[2] * u[8] - | ||
n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - | ||
5e-10 * Go * exp(-1.7 * Av) * u[9] | ||
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# 10: CO | ||
du[10] = n_H * (3.3e-5 * u[11] * u[3]) / T + | ||
n_H * 2e-10 * u[7] * u[8] - | ||
n_H * 1.7e-9 * u[10] * u[2] - | ||
n_H * 1.6e-9 * u[10] * u[5] + | ||
n_H * 5.8e-12 * (T^0.5) * u[9] * u[6] - | ||
1e-10 * Go * exp(-3 * Av) * u[10] + | ||
1.5e-10 * Go * exp(-2.5 * Av) * u[11] * shield | ||
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# 11: HCO+ | ||
du[11] = n_H * (-3.3e-5 * u[11] * u[3]) / T + | ||
n_H * 1e-9 * u[9] * u[12] + | ||
n_H * 1.7e-9 * u[10] * u[2] - | ||
1.5e-10 * Go * exp(-2.5 * Av) * u[11] | ||
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# 12: C+ | ||
du[12] = n_H * (-1.4e-10 * u[3] * u[12]) / (T^0.61) - | ||
n_H * 4e-16 * u[1] * u[12] - | ||
n_H * 1e-9 * u[9] * u[12] + | ||
n_H * 1.6e-9 * u[10] * u[5] + | ||
3e-10 * Go * exp(-3 * Av) * u[6] | ||
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# 13: M+ | ||
du[13] = n_H * (-3.8e-10 * u[13] * u[3]) / (T^0.65) + | ||
n_H * 2e-9 * u[2] * u[14] | ||
+ 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction | ||
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# 14: M | ||
du[14] = n_H * (3.8e-10 * u[13] * u[3]) / (T^0.65) - | ||
n_H * 2e-9 * u[2] * u[14] | ||
- 2.0e-10 * Go * exp(-1.9 * Av) * u[14] # this term was added as part of the skipped photoreaction | ||
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end | ||
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u0 = [0.5 ; # 1: H2 yep? | ||
9.059e-9 ; # 2: H3+ yep | ||
2.0e-4 ; # 3: e yep | ||
0.1 ; # 4: He SEE lines 535 NL99 | ||
7.866e-7 ; # 5: He+ yep? should be 2.622e-5 | ||
0.0 ; # 6: C yep | ||
0.0 ; # 7: CHx yep | ||
0.0004 ; # 8: O yep | ||
0.0 ; # 9: OHx yep | ||
0.0 ; # 10: CO yep | ||
0.0 ; # 11: HCO+ yep | ||
0.0002 ; # 12: C+ yep | ||
2.0e-7 ; # 13: M+ yep | ||
2.0e-7 ] # 14: M yep | ||
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tspan = (0.0, 30 * 3.16e10) # ~30 thousand yrs | ||
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prob = ODEProblem(Nelson_ODE, u0, tspan) | ||
refsol = solve(prob, Vern9(), abstol=1e-14, reltol=1e-14) | ||
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using Plots | ||
plot(sol; yscale=:log10, idxs = (0,5)) | ||
``` | ||
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## Run Benchmark | ||
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```julia | ||
abstols = 1.0 ./ 10.0 .^ (8:10) | ||
reltols = 1.0 ./ 10.0 .^ (8:10) | ||
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sol = solve(prob, DP8(), abstol=1e-8, reltol=1e-8) | ||
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setups = [Dict(:alg=>DP8()) | ||
Dict(:alg=>Vern7()) | ||
Dict(:alg=>CVODE_Adams()) | ||
Dict(:alg=>ARKODE(Sundials.Explicit(),order=6)) | ||
Dict(:alg=>lsoda()) | ||
Dict(:alg=>odex()) | ||
Dict(:alg=>ddeabm()) | ||
] | ||
wp = WorkPrecisionSet(prob,abstols,reltols,setups;appxsol=refsol,save_everystep=false, print_names = true) | ||
plot(wp) | ||
``` |