Evaluate time-dependent tendencies at correct time for each RK4 stage

[sbrus89]

This PR corrects a longstanding issue with RK4 and tendency terms which have an explicit time dependence (see #5364 and MPAS-Dev/MPAS-Model#375). Big thanks to @gcapodag and @jeremy-lilly for providing the fix in their LTS development branch linked in #5364.

Here, I have migrated these changes from their MPAS-Dev branch to E3SM and added the modifications to correct the convergence issues for the manufactured solution test case: E3SM-Project/polaris#72

[sbrus89]

Testing:

With this PR, the manufactured solution test case in Polaris converges at 2nd order when refining in space/time:

When refining in time only, 4th order convergence is achieved:

However, I have not been able to reproduce the 4th order convergence for the hurricane test case from Lilly et al. 2023 (Figure 4). The best I have been able to achieve is first order:

For this result, I ran from 2012-10-13_00:00:00 to 2012-10-13_01:00:00 starting from a 2012-10-13_00:00:00 restart file. I used dt=0.1 as a reference solution.

[sbrus89]

Closing to fix branch name.

[gcapodag]

Testing:

With this PR, the manufactured solution test case in Polaris converges at 2nd order when refining in space/time:

When refining in time only, 4th order convergence is achieved:

However, I have not been able to reproduce the 4th order convergence for the hurricane test case from Lilly et al. 2023 (Figure 4). The best I have been able to achieve is first order: For this result, I ran from 2012-10-13_00:00:00 to 2012-10-13_01:00:00 starting from a 2012-10-13_00:00:00 restart file. I used dt=0.1 as a reference solution.

@jeremy-lilly 👀

[sbrus89]

Moved to #6695