### Re: [deal.II] Geometric Conservation Law

Dear Martin or whom it may concern, I have solved the previous problem and am confirming that the conservative curl form has now been implemented and passes 2 complicated tests for GCL on symmetric and non-symmetric curvilinear grids for different polynomial degrees. Turns out that we did not

### Re: [deal.II] Geometric Conservation Law

Dear Martin, As an update, I figured out a way to have it work in 3D without needing to use another Evaluate call. The only issue is that I need the quadrature in the reference element since I construct an FE_DQGArbitraryNodes to evaluate the derivative (I do this since the metric Jacobian is

### Re: [deal.II] Geometric Conservation Law

Dear Martin, I would like to start by thanking you for all of your help. Here is a link to my fork: https://github.com/AlexanderCicchino/dealii It is not fully working yet, I need your help for the "evaluate" as you mentioned earlier. I have been trying multiple different ways but cannot seem

### Re: [deal.II] Geometric Conservation Law

Dear Alex, Great! I would suggest to start by simply adding new code to the maybe_update_q_points_Jacobians_... function with the option to turn it off or on. Depending on how the final implementation will look like we might want to move that to a separate place, but I think it will be less

### Re: [deal.II] Geometric Conservation Law

Dear Martin, Thank you very much! I have been working on making the test case not depend on our in house flowsolver's functions. I think that implementing Eq. 36 the "conservative curl" form would be sufficient. Yes this procedure sounds perfect to me, and I agree with the dimension of the

### Re: [deal.II] Geometric Conservation Law

Dear Alex, Great! The first thing we need to know is the equation. I had a quick look in the paper by Kopriva and I think we want to use either equation (36) or (37), depending on whether we consider the conservative or invariant curl form, respectively. In either case, it appears that we

### Re: [deal.II] Geometric Conservation Law

Dear Martin, Thank you for your response. Yes I agree that only some local computations are necessary to implement the identities. Yes I would be interested in this feature and trying to implement it. Do you have any suggestions on where I should start and overall practices I should follow?

### Re: [deal.II] Geometric Conservation Law

Dear Alex, This has been on my list of things to implement and verify with deal.II over a range of examples for quite a while, so I'm glad you bringing the topic up. It is definitely true that our way to define Jacobians does not take those identities into account, but I believe we should add

### Re: [deal.II] Geometric Conservation Law

Thank you for responding Wolfgang Bangerth. The GCL condition comes from the discretized scheme satisfying free-stream preservation. I will demonstrate this for 2D below, (can be interpreted for spectral, DG, finite difference, finite volume etc): Consider the conservation law: \frac{\partial

### Re: [deal.II] Geometric Conservation Law

Alexander, I am wondering if anybody has also found that the inverse of the Jacobian from FE Values, with MappingQGeneric does not satisfy the Geometric Conservation Law (GCL), in the sense of: Kopriva, David A. "Metric identities and the discontinuous spectral element method on