add Nelson benchmark equations

Author: ChrisRackauckas

benchmarks/AstroChem/nelson.jmd

@@ -0,0 +1,173 @@
+---
+title: Nelson Work-Precision Diagrams
+author: Stella Offner and Chris Rackauckas
+---
+
+```julia
+using OrdinaryDiffEq
+using Plots
+using Sundials
+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
+
+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)
+refsol = solve(prob, Vern9(), abstol=1e-14, reltol=1e-14)
+
+using Plots
+plot(sol; yscale=:log10, idxs = (0,5))
+```
+
+## Run Benchmark
+
+```julia
+abstols = 1.0 ./ 10.0 .^ (8:10)
+reltols = 1.0 ./ 10.0 .^ (8:10)
+
+sol = solve(prob, DP8(), abstol=1e-8, reltol=1e-8)
+
+
+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)
+```