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Compose Operators for Cylindrical and Spherical Coordinate Systems #341

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kkakosim opened this issue Mar 6, 2021 · 0 comments
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@kkakosim
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kkakosim commented Mar 6, 2021

I would like to compose multiple CenteredDifference operators to construct a PDE for cylindrical (and spherical coordinate) systems:

PDE

e.g. for the first term of the expression (and based on the heat_equation example)

Δ = CenteredDifference(ord_deriv, ord_approx, h, nknots)
bc = Dirichlet0BC(Float64)
step(f, p, t) =1/r^2 * Δ * ( 1/r * Δ * bc * f)
prob = ODEProblem(step, u0, (t0, t1))
alg = KenCarp4()
sol = solve(prob, alg)

I have tried multiple combinations but no luck.

EDITED: I also tried the nolineardiffusion function but I couldn't get the latest release of DiffEqOperators.jl to work

I got the latest version (v4.22) to work, and it seems that I can combine the ModelingToolkit operators (using Automatic Differentiation). Didn't verify yet with analytic solution.
eq = Dt(u(t,x)) ~ (1/x^2) * Dx( (1/x^2) * Dx(u(t,x)))
I still wonder if it is possible with the DiffEqOperators.

thanks

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