/
outer_ss_example.jl
165 lines (146 loc) · 5.55 KB
/
outer_ss_example.jl
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using NbodyGradient, LinearAlgebra
export State
#include("../src/ttv.jl")
#include("/Users/ericagol/Software/TRAPPIST1_Spitzer/src/NbodyGradient/src/ttv.jl")
# Specify the initial conditions for the outer solar
# system
#n=6
n=5
xout = zeros(3,n)
# Positions at time September 5, 1994 at 0h00 in days (from Hairer, Lubich & Wanner
# 2006, Geometric Numerical Integration, 2nd Edition, Springer, pp. 13-14):
xout .= transpose([-2.079997415328555E-04 7.127853194812450E-03 -1.352450694676177E-05;
-3.502576700516146E+00 -4.111754741095586E+00 9.546978009906396E-02;
9.075323061767737E+00 -3.443060862268533E+00 -3.008002403885198E-01;
8.309900066449559E+00 -1.782348877489204E+01 -1.738826162402036E-01;
1.147049510166812E+01 -2.790203169301273E+01 3.102324955757055E-01]) #;
#-1.553841709421204E+01 -2.440295115792555E+01 7.105854443660053E+00])
vout = zeros(3,n)
vout .= transpose([-6.227982601533108E-06 2.641634501527718E-06 1.564697381040213E-07;
5.647185656190083E-03 -4.540768041260330E-03 -1.077099720398784E-04;
1.677252499111402E-03 5.205044577942047E-03 -1.577215030049337E-04;
3.535508197097127E-03 1.479452678720917E-03 -4.019422185567764E-05;
2.882592399188369E-03 1.211095412047072E-03 -9.118527716949448E-05]) #;
#2.754640676017983E-03 -2.105690992946069E-03 -5.607958889969929E-04]);
# Units of velocity are AU/day
# Specify masses, including terrestrial planets in the Sun:
m = [1.00000597682,0.000954786104043,0.000285583733151,
0.0000437273164546,0.0000517759138449] #,6.58086572e-9];
# Compute the center-of-mass:
vcm = zeros(3);
xcm = zeros(3);
for j=1:n
vcm .+= m[j]*vout[:,j];
xcm .+= m[j]*xout[:,j];
end
vcm ./= sum(m);
xcm ./= sum(m);
# Adjust so CoM is stationary
for j=1:n
vout[:,j] .-= vcm[:];
xout[:,j] .-= xcm[:];
end
struct CartesianElements{T} <: NbodyGradient.InitialConditions{T}
x::Matrix{T}
v::Matrix{T}
m::Vector{T}
nbody::Int64
end
ic = CartesianElements(xout,vout,m,5);
function NbodyGradient.State(ic::NbodyGradient.InitialConditions{T}) where T<:AbstractFloat
n = ic.nbody
x = copy(ic.x)
v = copy(ic.v)
jac_init = zeros(7*n,7*n)
xerror = zeros(T,size(x))
verror = zeros(T,size(v))
jac_step = Matrix{T}(I,7*n,7*n)
dqdt = zeros(T,7*n)
dqdt_error = zeros(T,size(dqdt))
jac_error = zeros(T,size(jac_step))
rij = zeros(T,3)
a = zeros(T,3,n)
aij = zeros(T,3)
x0 = zeros(T,3)
v0 = zeros(T,3)
input = zeros(T,8)
delxv = zeros(T,6)
rtmp = zeros(T,3)
return State(x,v,[0.0],copy(ic.m),jac_step,dqdt,jac_init,xerror,verror,dqdt_error,jac_error,n,
rij,a,aij,x0,v0,input,delxv,rtmp)
end
function compute_energy(m::Array{T,1},x::Array{T,2},v::Array{T,2},n::Int64) where {T <: Real}
KE = 0.0
for j=1:n
KE += 0.5*m[j]*(v[1,j]^2+v[2,j]^2+v[3,j]^2)
end
PE = 0.0
for j=1:n-1
for k=j+1:n
PE += -NbodyGradient.GNEWT*m[j]*m[k]/norm(x[:,j] .- x[:,k])
end
end
ang_mom = zeros(3)
for j=1:n
ang_mom .+= m[j]*cross(x[:,j],v[:,j])
end
return KE,PE,ang_mom
end
# Now, integrate this forward in time:
hgrid = [1.5625,3.125,6.25,12.5,25.0,50.0,100.0,200.0]
nstepgrid = [32000000,16000000,8000000,4000000,2000000,1000000,500000,250000]
nskip = [128,64,32,16,8,4,2,1]
#h = 200.0 # 200-day time-step chosen to be <1/20 of the orbital period of Jupiter
#h = 100.0 # 100-day time-step chosen to check conservation of energy/angular momentum with time step
#h = 50.0 # 50-day time-step chosen to check conservation of energy/angular momentum with time step
h = 25.0 # 25-day time-step chosen to check conservation of energy/angular momentum with time step
#h = 12.5 # 12.5-day time-step chosen to check conservation of energy/angular momentum with time step
#h = 6.25 # 6.25-day time-step chosen to check conservation of energy/angular momentum with time step
#h = 3.125 # 3.125-day time-step chosen to check conservation of energy/angular momentum with time step
#h = 1.5625 # 1.5625-day time-step chosen to check conservation of energy/angular momentum with time step
# 50 days x 1e6 time steps ~ 137,000 yr (takes about 15 seconds to run)
grad = false
nstep = maximum(nstepgrid)
ngrid = 8
xsave = zeros(3,n,nstep,ngrid)
vsave = zeros(3,n,nstep,ngrid)
PE = zeros(nstep,ngrid); KE=zeros(nstep,ngrid); ang_mom = zeros(3,nstep,ngrid)
telapse = zeros(ngrid)
for j=1:8
h = hgrid[j]
nstep = nstepgrid[j];
s = State(ic)
pair = zeros(Bool,s.n,s.n)
if grad; d = Derivatives(T,s.n); end
# Set up array to save the state as a function of time:
# Save the potential & kinetic energy, as well as angular momentum:
# Time the integration:
tstart = time()
# Carry out the integration:
for i=1:nstep
if grad
ahl21!(s,d,h,pair)
else
ahl21!(s,h,pair)
end
xsave[:,:,i,j] .= s.x
vsave[:,:,i,j] .= s.v
KE_step,PE_step,ang_mom_step=compute_energy(s.m,s.x,s.v,n)
KE[i,j] = KE_step
PE[i,j] = PE_step
ang_mom[:,i,j] = ang_mom_step
end
s.t[1] = h*nstep
telapse[j] = time()- tstart
println("h: ",h," nstep: ",nstep," time: ",telapse[j])
end
using PyPlot,Statistics
for j=8:-1:1
plot(collect(1:1:nstepgrid[j])*hgrid[j],KE[1:nstepgrid[j],j] .+ PE[1:nstepgrid[j],j]); println(j," ",hgrid[j]," ",std(KE[1:nstepgrid[j],j] .+ PE[1:nstepgrid[j],j])); Emean[j] = mean(KE[1:nstepgrid[j],j] .+ PE[1:nst
end
read(stdin,Char)
clf()
loglog(hgrid,(Emean .- minimum(Emean)) ./abs(minimum(Emean)) ,"o")
loglog(hgrid,(Emean[8] .- minimum(Emean) ) ./abs(minimum(Emean)) .* (hgrid ./ hgrid[8]).^4 )
xlabel("Time step [d]")
ylabel("Fractional change in mean energy")