Updated cfl number calculation

[warisa-r]

Here, I implemented a new constructor of StepsizeCallback to take in ode and ode_algorithm so that the CFL number can be calculated before the simulation.

What can also be done if you deem necessary is to loop through every time step, calculate the CFL number of every time step and set the CFL number of the simulation as the smallest CFL in the loop. But since the max_dt of the current example is constant throughout the simulation, this is trivial in elixir_advection_perk2.

• add a test for new example
• change cfl in new example to cfl_opt

[github-actions]

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[DanielDoehring]

Thanks a lot! The functionality seems to be already there, now we just do some re-design.

[warisa-r]

I recently just tested this with PERK3 example and it works for

ode_algorithm = Trixi.PairedExplicitRK3(7, tspan, semi)
cfl = Trixi.calculate_cfl(ode_algorithm, ode)
stepsize_callback = StepsizeCallback(cfl = cfl)

And the lower number of stages like 6. But for the higher number of stages, the CFL number gets too large and linf and l2 error unfortunately becomes NaN/Inf.

[DanielDoehring]

I recently just tested this with PERK3 example and it works for

ode_algorithm = Trixi.PairedExplicitRK3(7, tspan, semi)
cfl = Trixi.calculate_cfl(ode_algorithm, ode)
stepsize_callback = StepsizeCallback(cfl = cfl)

And the lower number of stages like 6. But for the higher number of stages, the CFL number gets too large and linf and l2 error unfortunately becomes NaN/Inf.

This is somewhat expected, as for a nonlinear problem the spectrum itself slightly changes over the course of a simulation. If you decrease the supplied cfl slightly below the optimal one, i.e.,

cfl_opt = Trixi.calculate_cfl(ode_algorithm, ode)
stepsize_callback = StepsizeCallback(cfl = 0.9 * cfl_opt)

I would hope that the simulation runs.

[warisa-r]

I recently just tested this with PERK3 example and it works for

ode_algorithm = Trixi.PairedExplicitRK3(7, tspan, semi)
cfl = Trixi.calculate_cfl(ode_algorithm, ode)
stepsize_callback = StepsizeCallback(cfl = cfl)

And the lower number of stages like 6. But for the higher number of stages, the CFL number gets too large and linf and l2 error unfortunately becomes NaN/Inf.

This is somewhat expected, as for a nonlinear problem the spectrum itself slightly changes over the course of a simulation. If you decrease the supplied cfl slightly below the optimal one, i.e.,

cfl_opt = Trixi.calculate_cfl(ode_algorithm, ode)
stepsize_callback = StepsizeCallback(cfl = 0.9 * cfl_opt)

I would hope that the simulation runs.

Got it! Thank you for the explanation!
I just want you to know that I just tested this. Unfortunately, the simulation fails with the scale factor of 0.9 but for 0.85 it runs just fine.

[warisa-r]

If everything is good to go here, I will open a draft PR in Trixi.jl. Please let me know if you want anything else changed! @DanielDoehring

[DanielDoehring]

If everything is good to go here, I will open a draft PR in Trixi.jl. Please let me know if you want anything else changed! @DanielDoehring

Yeah let's move to the original repo!