FFSL linear model transport

[James Kent (jameskent-metoffice)]

PR Summary

Sci/Tech Reviewer: cjohnson-pi
Code Reviewer:

The linear model currently uses MoL transport. Using FFSL should improve performance and mean we use the same transport scheme for linear and non-linear transport.

This PR has added the tangent linear FFSL code. I have created the control routines for horizontal and vertical transport, and then used the existing FFSL kernels. This builds on the split transport routine added in PR#149.

The linear transport has two parts, u' dot grad(ls_f) and ls_u dot grad(f'). For the u' dot grad(ls_f) term, as this is a flux-form semi-Lagrangian method, we need to first transport ls_f by ls_u, and then compute the flux using u' with this. This is documented in the code.

I have added a C12 test using FFSL (for both azspice and ex1a) and also a C224 test. The C224 test is run with a smaller dt than the MoL version - this is due to the stability of FFSL depending on the Lipschitz number and any stability fixes we use being non-linear in nature.

Results for C12 NWP Linear Model Test:

This is MoL on trunk showing u:

This is FFSL showing u:

This is MoL on trunk showing theta:

This is FFSL showing theta:

FFSL has produced larger velocities and theta values near the model top.

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trac.log

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