Allow single-step backward Euler integrator

[chongchonghe]

This allows the user to use a single-step Backward Euler integrator, ignoring its accuracy. There are situations where we control relative error by setting the hydro/radiation timestep, and in a reaction network we simply want a backward Euler solve and don't care about error.

To force the BackwardEuler integrator to do a single-step integration, set integrator.do_single_step = 1.

Verified with the burn_cell unit test:

cd unit_test/burn_cell
make INTEGRATOR_DIR=BackwardEuler
echo "integrator.do_single_step = 1" >> inputs_aprox13
./main3d.gnu.ex inputs_aprox13 

Context: this is part of the effort to couple multi-group radiation hydrodynamics with thermochemistry in Quokka.

Addresses #1771

[zingale]

can you also add a note to the docs here:
https://github.com/AMReX-Astro/Microphysics/blob/main/Docs/source/ode_integrators.rst

[chongchonghe]

can you also add a note to the docs here: https://github.com/AMReX-Astro/Microphysics/blob/main/Docs/source/ode_integrators.rst

Done.

[zingale]

you also need to fix the style CI failures -- it looks like you used tabs and have trailing whitespace.

[zingale]

also, rather than making atol_enuc special (e.g., why is this set to -1 and not the others?) it might be better to simply define a new parameter in Microphysics/integration/BackwardEuler/_parameters, like do_single_step that defaults to 0, but if set to 1 does what you want.

I think that would be cleaner.

[chongchonghe]

@zingale I've added a integrator.do_single_step parameter to toggle single-step EU. I tested it on my computer and it worked fine. We don't have a unit test for this yet, because I don't know how to make a test problem use BackwardEuler without manually modify CMakeLists.txt in the root directory (see #1772 ).

[zingale]

you can test it with GNU make -- we don't use cmake. Just do:

make INTEGRATOR_DIR=BackwardEuler

in the test directory.

[chongchonghe]

you can test it with GNU make -- we don't use cmake. Just do:

make INTEGRATOR_DIR=BackwardEuler

in the test directory.

Thanks, that works. I kept the changes minimal and it works just fine.

[zingale]

there are also still CI style failures.

[chongchonghe]

there are also still CI style failures.

Fixed.