Compute a worldtube constraint for Klein-Gordon Cce

[Sizheng-Ma]

Proposed changes

Both Cauchy and characteristic systems evolve the scalar field independently. The results have to be consistent at the worldtube. This yields a worldtube constraint (Cce::Tags::KleinGordonWorldtubeConstraint) that needs to be monitored during evolution, which reads:

$C=\psi^{\rm Cauchy}-\psi^{\rm Characteristic}$,

where $\psi^{\rm Cauchy}$ is from Cauchy's worldtube data (Cce::Tags::BoundaryValue<Cce::Tags::KleinGordonPsi>) and $\psi^{\rm Characteristic}$ is the evolved variable (Cce::Tags::KleinGordonPsi).

This PR adds an action to compute Cce::Tags::KleinGordonWorldtubeConstraint and dump it to the disk. The first commit adds its tag. The second one initializes the tag in the databox. The third commit adds the action. And the last one dumps the tag to the disk.

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Further comments

[wthrowe]

This doesn't appear to have anything to do with gauge transformations, so it should probably go in a different file.

[Sizheng-Ma]

I've moved the mutator to a new file.

[wthrowe]

This needs a test that actually checks that the result. The current test just checks that db::mutate_apply<ComputeKGWorldtubeConstraint> and ::Actions::MutateApply<ComputeKGWorldtubeConstraint> give the same answer, which doesn't give much evidence that it is the correct answer.

[Sizheng-Ma]

Testing the physical aspect of the calculation is a quite nontrivial task. In fact, it will be one of the main focuses of the upcoming method paper for this CCE system --- in the paper, a variety of systems are used to show that the constraint converges exponentially with resolution (I've obtained many solid results to verify this is indeed the case). Another PR #5932 initiates the steps to build worldtube data for those systems. The goal therein is to add a new executable (in parallel with AnalyticTestCharacteristicExtract) that can justify all the physical aspects of the new CCE system, including the worldtube constraint in this PR.

[wthrowe]

I'm not concerned about the physics, here. I want some evidence that the variable slicing is doing what you expect. At the moment, all the test does is checks that the function will run without crashing.

[knelli2]

@Sizheng-Ma I believe what @wthrowe is looking for is just a test where you give the apply function a random cauchy KG Psi, volume Psi, and an interpolator, and you check that you get out an expected value (since it's just a subtraction).

[wthrowe]

Yes, that would be fine.

[knelli2]

@Sizheng-Ma I believe what @wthrowe is looking for is just a test where you give the apply function a random cauchy KG Psi, volume Psi, and an interpolator, and you check that you get out an expected value (since it's just a subtraction).