I have a question regarding the order of accuracy of the ACM method; Have you done any tests using the method of manufactured solutions ( published or otherwise) ?
I tried the 2D taylor green benchmark but the order of accuracy I am getting is nowhere near what it should be. When comparing with exact solution I used the solution points directly not the subdivided solution in the vtu file to avoid interpolation issues polluting the order of accuracy
Also regarding the ACM, how would one obtain the residual of the continuity and momentum equations? Pseudo-stats only report the change between two consecutive pseudo iterations
It is a double periodic 2D manufactured solution case, the u, v source terms are evaluated using Mathematica
I attach the ini file here
The Re = 10
I calculated the order of accuracy in the manner described in the article which is fairly straightforward
where eps_k is the difference between the exact solution and the numerical solution.
I used the same meshes resolutions as the article 4x4, 8x8, 16x16, 32x32 with double periodic bcs generated using gmsh
For now, I am only trying to verify the spatial accuracy so following the article’s example I am using very small dt
I tried different zeta values, different pseudo-dt, more pseudo-niters-max going as high as 50 which is killing my performance
the only part I did not mess with is the LDG beta and tau
I double-checked the source terms several times but it seems okay
So I am not sure what could be the problem.
I am a little confused as to the test case you are using.
The 2D TGV case in the paper you reference does not seem to use a method of manufactured solutions, it just solves the regular NS equations without a source term?
Hi Peter,
You’re right. I left the source term in the ini file because it may not evaluate to zero depending on the choice of the length scale in the Reynolds number (since the domain is not a unit square). When the length scale is chosen to be 1 ( Re = 1/nu) which is the case in all of our simulations so far, then the source term vanishes and that’s what’s used in the ini file attached.
So I don’t think that the source term is the cause of the problem. I removed it now just in case but I got the exact same results.
How small is the dt that you are using, and do the numbers change when you reduce it further?
The time step dt = 0.001 when decreased to 5e-4 and even 1e-4 the change in error is no more 1%
pseudo-niters-max = 50 , using p-multigrid with vermiere pseudo integration
I tried local-pi but it was either unstable or ineffective perhaps I need to do needs some fine-tuning of my chosen parameters
What do you mean quantitatively by ‘killing performance’
Are you using local pseudo dt and PMG etc. for the inner iterations, or just plain RK4?
As for the matter of performance, using p-multigrid with pseudo-niters-max of 50 yields a wall clock time of 6 hours if dt is taken as low as 1e-4 for 8x8 mesh to run only 1s ( GPU utilization at less than 15%)
Can you send plots of how the pseudo residuals are converging in each dt?
As for the residuals:
p : 5e-5 ~ 1e-4
uv: 1e-6 ~ 1e-7
For reference, the residual history data and the corresponding ini file can be downloaded from the following link https://mega.nz/folder/jVZBwIBb#gk6J1zSTM-Hg8GgRzDYysw
I included residual history for 0.25s only
