Revive SSPKnoth #292
Revive SSPKnoth #292
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@dennisYatunin this is ready for review when you have time |
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| Refer to the documentation for the precise meaning of the symbols below. | ||
| """ | ||
| struct RosenbrockTableau{N} |
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I'd like to keep the tableau structs confined to the minimal set of values needed to define a timestepping scheme, and to have all values generated from those confined to the cache. The ExplicitTableau (which I'll rename to ButcherTableau in the reformulation) has the vector b, which you defined elsewhere in this file, and the matrix A, which corresponds to your matrices α and Γ. The ExplicitTableau also has the vector c, which I think corresponds to the values αi and γi that you compute in your stage loop; it might be worth pre-computing those here as well. So, maybe the constructor here can look something like RosenbrockTableau(α, Γ, b, c = sum(α, dims = 2), γ = sum(Γ, dims = 2))?
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I added constructor that takes alpha, Gamma, and b. Maybe we can refine things once we work with the reformulation?
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Documentation fails, but also fails on main with the same error. This is probably #283. I'll go ahead and merge this. I'll also refine the tableau when things are a little bit more clear for the reformulation. |
This PR brings back SSPKnoth. In its current incarnation, SSPKnoth is a 2nd-order Rosenbrock method that does not require a Newton solver. The implementation was tested with a series of convergence tests and in ClimaAtmos. The convergence tests show the expected order of convergence when SSPKnoth is used fully implicitely with the correct Jacobian. This is not the case when the the Jacobian is approximated.
In ClimaAtmos, I investigated maximium timestep and best dissipation parameters for baroclinic waves. I found that the CAM_SE parameters work well and yield a maximum timestep of 200s for our target resolution (30 horizontal elements, 63 verfical ones).
In this PR, I also fixed a couple of small things that outdated.
I also added a general tutorial on how to use ClimaTimeSteppers, but the tutorial should be expanded with more information and explanations by those who know how things work.
Closes #276