Fix Adams-Bashforth scheme and some further tidy-up for the TimeIntegration class and subclasses.

Issue/feature addressed

There is a problem with the start-up phase of Adams-Bashforth time-integration schemes from problems with time-depend boundary condition. Additionally v_GetTimeStability virtual functions are updated with proper/consistent values from stability analysis.

Proposed solution

The start-up problem results from improper application of time-dependent boundary condition.

Implementation

Use function calls to DoProjection to apply the time-depend boundary condition.

Tests

Convergence studies have been conducted. Here are the convergence results:

AdamsBashforthOrder1:
1.0007604623907342
1.0003867433150533
1.000193410542337
AdamsBashforthOrder2:
2.0001137099540207
2.000016245010792
1.9999922023719916
AdamsBashforthOrder3:
3.0000170601303484
3.000049134302589
3.0000541588589678
AdamsBashforthOrder4:
4.429711169522635
4.029335517236484

Suggested reviewers

Please suggest any people who would be appropriate to review your code.

Notes

Please add any other information that could be useful for reviewers.

Checklist

• Functions and classes, or changes to them, are documented.
• [ ] User guide/documentation is updated.
• Changelog is updated.
• [ ] Suitable tests added for new functionality.
• Contributed code is correctly formatted. (See the contributing guidelines).
• [ ] License added to any new files.
• No extraneous files have been added (e.g. compiler output or test data files).