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Fixed up the Nelson ODE function #7

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nnd389 Oct 25, 2024
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Updated the nelson ODE function, (made it nicer to look at) and added…
nnd389 Oct 25, 2024
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Updated the nelson ODE function, (made it nicer to look at) and added…
nnd389 Oct 25, 2024
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Updated the nelson ODE function, (made it nicer to look at) and added…
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288 changes: 160 additions & 128 deletions dev/AstroChem/nelson/index.html
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300 changes: 161 additions & 139 deletions markdown/AstroChem/nelson.md
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
---
author: "Stella Offner and Chris Rackauckas"
author: "Nina De La Torre (Advised by Stella Offner) and Chris Rackauckas"
title: "Nelson Work-Precision Diagrams"
---
```julia
Expand All @@ -11,151 +11,173 @@ using ODEInterface, ODEInterfaceDiffEq


```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

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

# 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]

# 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


# 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

# 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

# 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

# 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)

# 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

# 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]

# 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

# 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]

# 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]

# 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

# 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
#=
The ODE function defined below models the reduced carbon-oxygen
chemistry network of Nelson & Langer (1999, ApJ, 524, 923).

This Julia ODE function was written by Nina De La Torre advised by Dr. Stella Offner.
The solution was compared with results derived by DESPOTIC, (Mark Krumholz, 2013)
a code to Derive the Energetics and Spectra of Optically Thick Insterstellar Clouds.
DESPOTIC has pre-defined networks, one of them coming from the Nelson & Langer paper,
so the initial conditions and parameters were meant to mimic those from DESPOTIC.

Parameter definitions:
T = 10 --> Tempurature (Kelvin)
Av = 2 --> V-Band Extinction
G₀ = 1.7 --> Go; "a factor that determines the flux of FUV radiation relative to the standard interstellar value (G₀ = 1) as reported by Habing (1968)."
n_H = 611 --> Hydrogen Number Density
shield = 1 --> "CO self-shielding factor of van Dishoeck & Black (1988), taken from Bergin et al. (1995)"
=#

function Nelson!(du,u,p,t)
T, Av, Go, n_H, shield = p

# 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]

# 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]

# 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]
+ 2.0e-10 * Go * exp(-1.9 * Av) * u[14]

# 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]

# 5: He+
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]

# 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

# 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)

# 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

# 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]

# 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

# 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]

# 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]

# 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]

# 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]

end


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


tspan = (0.0, 30 * 3.16e10) # ~30 thousand yrs

prob = ODEProblem(Nelson_ODE, u0, tspan)
# Set the Timespan, Parameters, and Initial Conditions
seconds_per_year = 3600 * 24 * 365
tspan = (0.0, 30000 * seconds_per_year) # ~30 thousand yrs

params = (10, # T
2, # Av
1.7, # Go
611, # n_H
1) # shield

u0 = [0.5, # 1: H2
9.059e-9, # 2: H3+
2.0e-4, # 3: e
0.1, # 4: He
7.866e-7, # 5: He+
0.0, # 6: C
0.0, # 7: CHx
0.0004, # 8: O
0.0, # 9: OHx
0.0, # 10: CO
0.0, # 11: HCO+
0.0002, # 12: C+
2.0e-7, # 13: M+
2.0e-7] # 14: M


prob = ODEProblem(Nelson!, u0, tspan, params)
refsol = solve(prob, Vern9(), abstol=1e-14, reltol=1e-14)
sol2 = solve(prob, FBDF())
sol3 = solve(prob, QNDF())
sol4 = solve(prob, CVODE_BDF())
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Is there a reason for using the high tolerances here? That's almost certainly the reason why they are different from the reference.


using Plots
plot(sol; yscale=:log10, idxs = (0,5))
```

using Plots
colors = palette(:acton, 5)
p1 = plot(refsol, vars = (0,11), lc=colors[1], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ Reference solution")
p2 = plot(sol2, vars = (0,11), lc=colors[2], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using FBDF")
p3 = plot(sol3, vars = (0,11), lc=colors[3], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using QNDF")
p4 = plot(sol4, vars = (0,11), lc=colors[4], legend = false, titlefontsize = 12, lw = 3, xlabel = "", title = "HCO+ solved using CVODE FBDF")
combined_plot = plot(p1, p2, p3, p4, layout=(4, 1), dpi = 600, pallete=:acton)
display(combined_plot)
```
Error: UndefVarError: `sol` not defined
```


![](figures/nelson_compare.png)



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