Hey I am trying to solve a system of equations where my input parameters are altitude dependent values. These values should be supplied into system of equations after discretizing the equation. I have created an Interpolated function which has to be taken into the equations and has to solve. I made an example code here. Your help is appreciated.
using ModelingToolkit, DomainSets
using MethodOfLines, OrdinaryDiffEq
using Interpolations
using Symbolics: Num
using RuntimeGeneratedFunctions
Independent variables
@parameters t x
@variables u(..)
Correct Symbolic Definition: Callable symbolic parameter
@parameters D_param(..)
Differentials
Dt = Differential(t)
Dx = Differential(x)
=== INTERPOLATION SETUP ===
Grid
x_vals = 0.0:0.1:Float64(pi)
const XMAX = Float64(pi)
Parameter data (Diffusion coefficient)
D_vals = ones(length(x_vals)) * 0.1
Create Interpolation object
D_fun = LinearInterpolation(x_vals, D_vals, extrapolation_bc=Line())
Correct parameter dictionary input:
param_vals = Dict(D_param(x) => x → D_fun(x))
Goal: While discretization D_param(x) value should be taken from interpolated function while solving
PDE equation: Only includes the D(x) term
eqs = [
Dt(u(t,x)) ~ D_param(x) * Dx(Dx(u(t,x)))
]
Domains
tdom = Interval(0.0, 1.0)
xdom = Interval(0.0, XMAX)
domains = [t ∈ tdom, x ∈ xdom]
Boundary Conditions (BCs)
bcs = [
u(0.0, x) ~ sin(x), # IC at t=0
u(t, 0.0) ~ 1e-3, # BC at x=0
u(t, XMAX) ~ 0.0 # BC at x=π
]
Build PDESystem
@named pdesys = PDESystem(eqs, bcs, domains, [t,x], [u(t,x)], [D_param(x)];
defaults = param_vals );
discretization = MOLFiniteDifference([x => 10], t;approx_order = 2, use_ODAE = false)
sym_prob = symbolic_discretize(pdesys, discretization); ## I could see the discretized equations over 10 altitudes.
prob = discretize(pdesys, discretization);
prob has threw the following error:
The system of equations is:
Equation[Differential(t)((u(t))[2]) - (8.207015875029361(u(t))[1] - 16.414031750058722(u(t))[2] …
MethodError: Cannot convert an object of type var"#110#111" to an object of type Number
The function convert exists, but no method is defined for this combination of argument types.
Closest candidates are:
convert(::Type{Number}, !Matched::Unitful.Quantity)
@ Unitful ~/.julia/packages/Unitful/sxiHA/src/conversion.jl:166
convert(::Type{T}, !Matched::Union{Static.StaticBool{N}, Static.StaticFloat64{N}, Static.StaticInt{N}} where N) where T<:Number
@ Static ~/.julia/packages/Static/SeEGr/src/Static.jl:427
convert(::Type{T}, !Matched::Number) where T<:Number
@ Base number.jl:7
…
After this I have to do the following one
sol = solve(prob, Tsit5())