Update OmegaV1GoverningEqns.md

[hyungyukang]

This PR slightly modifies the Omega-V1 governing equation document OmegaV1GoverningEqns.md.

• Fix some bugs in formulations
• Update definition and units in Variable Definitions to match its usage in the document

Compiled version is here.

The code needs to be updated (e.g., changing LayerThickness to PseudoThickness) to match the document. I will open another PR for this.

Checklist

• Documentation:
  • Design document has been generated and added to the docs
  • Developer's Guide has been updated
  • Documentation has been built locally and changes look as expected

[hyungyukang]

The code needs to be updated (e.g., changing LayerThickness to PseudoThickness) to match the document. I will open another PR for this.

I found that this change would require many updates in both Omega and Polaris. I don’t think it’s necessary at this point, so we should keep using LayerThickness for $\tilde{h}$ and GeometricLayerThickness for $h$.

[mark-petersen]

@hyungyukang thanks for your attention to the documentation. This looks good to me.

[xylar]

@hyungyukang, I also noticed several issues with this document. Most are different from your changes but I think a few may overlap. After we merge your fixes, I would like to rebase #326 and have you take a look at that.

[xylar]

The code needs to be updated (e.g., changing LayerThickness to PseudoThickness) to match the document. I will open another PR for this.

I found that this change would require many updates in both Omega and Polaris. I don’t think it’s necessary at this point, so we should keep using LayerThickness for $\tilde{h}$ and GeometricLayerThickness for $h$.

I would be strongly in favor or renaming LayerThickness to PseudoThickness to avoid confusion in both Omega and Polaris. I will try to get the ball rolling, even knowing that this will be quite disruptive. It won't be better if we wait.

[xylar]

@hyungyukang and @vanroekel, could we get this finalized an merged? I would like to rebase #326 onto that merge and then I have yet another PR (#351) I'd like to make to revise the way the pressure-gradient term is handled. We ended up needing those revisions for our final implementation.

[hyungyukang]

@vanroekel, could you please review this PR? I’ve approved #326, and I think we can merge both PRs into develop and open another PR later if needed.

[vanroekel]

Thanks for the ping on this one - approving based on visual inspection

[xylar]

@vanroekel, can you merge this one? (You're the assignee.) Then, I can rebase and merge #326 later today.

[xylar]

@vanroekel, it looks like you didn't have time to get to this, which is totally fine. I'll take care of it now that I'm not on my phone :-).