Use ClimaTimeSteppers in implicit hydro balance example

[charleskawczynski]

This PR changes the implicit hydro balance example to use ClimaTimeSteppers.

This is a peel off from #1358.

This will technically have behavior changes because we're switching from Rosenbrock23 to ARS343

[charleskawczynski]

bors try

[bors]

try

Build succeeded!

The publicly hosted instance of bors-ng is deprecated and will go away soon.

If you want to self-host your own instance, instructions are here.
For more help, visit the forum.

If you want to switch to GitHub's built-in merge queue, visit their help page.

• lib-climacore-plots
• test-os (ubuntu-20.04)
• test-os (windows-latest)
• lib-climacore-vtk
• lib-climacore-makie
• lib-climacore-tempestremap
• buildkite/climacore-ci
• format
• docbuild

[charleskawczynski]

This is actually breaking (we're using soft_fail on this job)

[charleskawczynski]

@dennisYatunin, any suggestion on what to do here? What's the nearest neighbor change?

[dennisYatunin]

Ah, yes, I think passing Wfact = Wfact! to the ODEFunction should fix your error.

[charleskawczynski]

bors try

[bors]

try

Build failed:

• buildkite/climacore-ci

[dennisYatunin]

Oh, sorry, I was looking at the ClimaAtmos code. In this file, it would be Wfact = jacobian!. The jac = jacobian! is not used by ClimaTimeSteppers (because the thing we're actually specifying here is I - dt * gamma * J, rather than J itself).

[dennisYatunin]

Actually, looking more closely at this, I don't think that will work. The jacobian!(J, Y, p, t) function needs to be rewritten as a Wfact!(W, Y, p, dtγ, t) function (so J needs to be replaced with I - dtγ * J), and then linsolve! needs to be modified to solve A * x = b, where A = I - dtγ * J, instead of whatever it's solving now.

[charleskawczynski]

Superseded by #1400