CFL With Terrain

[AMLattanzi]

Summary

This PR resolves #3656. Additionally, and more importantly, it modifies the CFL constraint to be terrain aware. Consider the map for terrain following coordinates:

And linearize the set of equations

Employing the gradient and divergence relations for terrain, we may evaluate the flux Jacobian matrix and its eigenvalues:

The eigenvalues then yield the CFL constraint of:

NOTE: The tridiagonal solve will remove second order vertical derivatives, see g^{33}, in the metric tensor above. Therefore, the above relation may be further simplified and it will indeed increase the \delta t estimate. That closure has been implemented ONLY for substepping.

This write up demonstrates that the contravariant velocity omega must be used for the CFL estimation along with terrain metric terms. Finite u/v will dominate omega and may control the max stable time step. Additionally, steep terrain will also impact the max stable time step and no amount of implicit substepping will completely alleviate that since the implicit tridiagonal solve only alleviates second order vertical derivative terms and cross derivative terms still persist.