Non-split physics for all explicit or IMEX time discretisations #578
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tommbendall
added
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enhancement
| raise NotImplementedError( | ||
| 'Physics not implemented with RK schemes that use the ' | ||
| + 'predictor form') | ||
| evaluate(self.field_i[stage], self.dt) |
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Are we sure this is correct? It doesn't match the comment -- I thought we needed to sum over the source terms and this would be difficult to do
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I think this is correct, unless why understanding of evaluate is wrong.. We evaluate the physics terms in field_i from the previous stage, since field_i is a list we have all previous states for each stage. The physics terms (non-time derivative) are then in the rhs that goes into the solver.
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So the equation we are trying to solve is:
y^m = y^0 - dt*Sum_{i=0}^{m-1} a_{m,i} * F[y^i], for m = 1 to M - 1
What the evaluate method does is perform F[y] and put the value of that into a source field S. The thing that we don't have is M different source fields -- we only have one. So rather than having M source fields containing F[y^i] (for i=1 to m-1), and doing m-1 evaluations, we are overwriting S with ``F[y^{m-1}]` and not bringing in all of the correct contributions.
I don't think coding this is straightforward which is why I think it hasn't been done yet! But hopefully a test could demonstrate what is correct or not...
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| @pytest.mark.parametrize("timestepper", ["split", "nonsplit_imex_rk", "nonsplit_imex_sdc", |
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Could we also add the explicit with the 'predictor' method?
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| stepper.run(0, tmax=tmax) | ||
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| error = norm(stepper.fields('f') - f_end) / norm(f_end) |
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I don't know if this test is too slack? I think we are mainly testing the transport her and less testing whether the physics is correct.
Could we:
(a) check against the result from a split-physics time stepper (which would have the downside of being inefficient unless we make the split-physics value be a KGO)
or (b) find a coupled physics test with a known solution?
Co-authored-by: Thomas Bendall <[email protected]>
…t/gusto into nonsplit_physics
Currently you can only have physics when using IMEX RK, Explicit RK (Predictor) or IMEX SDC by using SpitPhysicsTimestepper. I will add the capability to do this, and a unit test to show it has the same results as SplitPhysicsTimestepper.