Add Roe-type flux #625
Add Roe-type flux #625
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jh66637
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| vector const & up, | ||
| vector const & n) const | ||
| { | ||
| return Number{0.5} * (pm + pp) + tau * (um * n - up * n); |
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@kronbichler: If I read your comment #587 (comment) correctly, this is the Roe-type flux you were describing. Is this correct?
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I must admit that I had to check carefully how the two fluxes are defined. I looked into http://dx.doi.org/10.1016/j.cma.2015.12.003 and formulas (18)-(20) in particular. What they call HDG flux should be the Roe flux. In your formula, I think both the local Lax-Friedrichs (Rusanov) flux and the Roe flux are the same, because it does not matter whether you switch the order of the subtraction and the multiplication u * n. Looking at the flux, they are the Roe flux both. For a Lax-Friedrichs that dissipates in all directions, you would need to take the outer product of u \otimes n and return that to the place of use instead of flux_mass * n. In other words, right now you contract between u and n, before you multiply by n again, but for Lax-Friedrichs you would need to contract between n and n, and afterwards multiply by u.
As these formulas are intricate and I might have missed some important detail, I recommend you to have another look in terms of literature and formulas, and decide how you want to proceed.
I guess right now you don't see a difference in any of the results, do you? While I would expect that for dim > 1, one should see a difference between Roe and Rusanov.
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I agree, that the fluxes are equivalent and the results are exactly the same.
Thank you for pointing out the paper, I didn't find helpful literature with the keyword Roe-type flux. With this, I can go through the equations in detail 👍
I will convert the PR to a draft until I find the time to do so.
Closes #588