OK – I used the DAE solver a year ago without problems. Now, it doesn’t work for me:
using Plots; pyplot();
using DifferentialEquations;
using Sundials;
If I run the example at DAE documentation, there are no problems – I get the expected solution.
Next, I try to solve a simple tank model with mass balance \frac{dm}{dt} = \dot{m}_i - \dot{m}_e (1) where the effluent by gravity is given by some Bernoulli model, \dot{m}_e = K\sqrt{\frac{h}{h^\varsigma}} (2), mass and volume are related by m=\rho V (3), and volume and level are related by V=Ah (4).
So… I have a DAE with 4 equations, (1)-(4) and 4 unknowns, w = [m,V,h,\dot{m}_e] – or w = [m,V,h,md_e] in Julia syntax. In addition, I have an input function \dot{m}_i(t) which I denote md_i(t), and four parameters \theta = [\rho, A, K, h^\varsigma] or p = [rho,A,K,h_s] in Julia.
In Julia, I specify the DAE model:
function tank(err,dw,w,p,t)
rho,A,K,h_s = p
m,V,h,md_e = w
dm = dw[1]
#
err[1] = md_i(t) - md_e - dm
err[2] = md_e - K*sqrt(h/h_s)
err[3] = m-rho*V
err[4] = V-A*h
end
#
diff_var = [true, false, false, false];
#
function md_i(t)
return 1.5
end
;
Next, I define values:
# Parameters
rho = 1. # kg/L
A = 5. # dm^2
K = 3. # kg/s
h_s = 4. # dm
p = [rho,A,K,h_s]
# Initial values, etc.
h0 = 1.5 # dm
V0 = A*h0
m0 = rho*V0
md_e0 = K*sqrt(h0/h_s)
#
w0 = [m0,V0,h0,md_e0]
dw0 = [0.0,0.0,0.0,0.0]
tspan = (0.0,50.0)
and finally specify the problem and solve the model:
prob = DAEProblem(tank,dw0,w0,tspan,differential_vars=diff_var)
#
sol = solve(prob,IDA())
Instead of getting an expected solution, I get a lengthy error message…
MethodError: no method matching iterate(::Nothing)
Closest candidates are:
iterate(!Matched::Core.SimpleVector) at essentials.jl:568
iterate(!Matched::Core.SimpleVector, !Matched::Any) at essentials.jl:568
iterate(!Matched::ExponentialBackOff) at error.jl:199
...
Stacktrace:
[1] indexed_iterate(::Nothing, ::Int64) at .\tuple.jl:66
[2] tank(::Array{Float64,1}, ::Array{Float64,1}, ::Array{...
I’m sure I’ve done a stupid mistake, but does anyone have a clue?
