Hello,
is there a particular reason for which entropy filtering is not compatible with adaptive time stepping?
Best regards
In general, it is difficult to identify whether differences in the solution due to different time steps are from time integration errors, errors stemming from spurious numerical oscillations around discontinuities which can grow w.r.t. time, or differences in the dissipation introduced by the shock capturing method (which is calculated discretely so may not converge monotonically w.r.t. decreasing time step). In addition, element-wise filtering methods tend to negatively affect adaptive time stepping methods regardless of whether they’re used adaptively and/or as a shock-capturing method (see “High-Order Implicit Large-Eddy Simulations of Flow over a NACA0021 Aerofoil” in AIAAJ). This is due to the irregularity introduced at the element interfaces (i.e., solution jumps) which tends to mess with the temporal error estimate. In practice, what this means is that the temporal error estimate from an adaptive RK scheme when coupled with entropy filtering will not be well-behaved and will spuriously overpredict the temporal integration error, lowering the time step much more than necessary. In the long term, we may look at downselecting the elements which are used for calculating the temporal integration error to just the elements without the filter active (and maybe something like a CFL-based time step limit on the filtered elements), but this is not something currently in the works.
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Thanks a lot for the very explanatory answer!