Diagnostics

We can add diagnostics to a FourierFlows's problem using Diagnostic functionality.

To demonstrate how we add diagnostics to a PDE problem, let's try to add one to the simple PDE problem we constructed in the Problem section. For example, say we'd like to add a diagnostic we refer to as the "energy" and which we define to be:

\[E = \int u^2 \, \mathrm{d} x .\]

After we have constructed the problem (prob) (see Problem section), we then create a function that takes prob as its argument returns the diagnostic:

using LinearAlgebra: ldiv!

function energy(prob)
    ldiv!(prob.vars.u, grid.rfftplan, prob.sol)

    return sum(prob.vars.u.^2) * prob.grid.dx
end

and then we create a Diagnostic using the Diagnostic constructor. Say we want to save energy every 2 time-steps, then:

E = Diagnostic(energy, prob, freq=2, nsteps=200)

Diagnostic
  ├─── calc: energy
  ├─── prob: FourierFlows.Problem{DataType, Vector{ComplexF64}, Float64, Vector{Float64}}
  ├─── data: 101-element Vector{Float64}
  ├────── t: 101-element Vector{Float64}
  ├── steps: 101-element Vector{Int64}
  ├─── freq: 2
  └────── i: 1

Now, when we step forward the problem we provide the diagnostic as the second positional argument in stepforward!:

stepforward!(prob, E, 200)

Doing so, the diagnostic is computed and saved at the appropriate frequency (prescribed by E.freq).

diag1 = Diagnostic(foo, prob)
diag2 = Diagnostic(bar, prob)

stepforward!(prob, [diag1, diag2], 1)

The times that the diagnostic was saved are gathered in E.t. Thus, we can easily plot the energy time-series, e.g.,

using CairoMakie

lines(E.t, E.data, axis = (xlabel = "time", ylabel = "energy"))