I am performing compressible flow analysis using entropy filter. When order = 4, it takes tens of times more (expected) calculation time than when applying artificial-viscosity shock-capturing.
So I’m going to use time controller for std formulation. It is judged that this is applied to both dimensionless and dimensionless settings.

However, when I use [dual, sdirk33&rk34, maxiter 10(~20) with artificial-visibility], the value of E (in residual.csv) is very different.
In dimensional run: E ~ 200 to 2000
In non-dimensional run : E ~ 0.8 to 2.0 (Non-dimensionalized sutherland law - #16 by YoonSuKyung)

Q1) Is it correct that it takes a lot of time non-physically when using an entry-filter?

Q2) I need to apply pi-controller, is there an appropriate value such as atol, rtol, etc?
It seems that the time controller is not being applied in the current setting. The current setting is a compressible flow of Re=5000 and M=0.4 with entropy-filter, and E is around 50,000,000.

Q3) Do developers perform calculation with dimensionless values? If you have an example of calculation, can you share the grid and setting file you used? (not 2d example case)

Step size control is not supported when running with entropy filtering. You will need to determine an appropriate time step by hand and stick with it. The RK45 solver is likely the most efficient.

The entropy filter, when one of the constraints is not met, takes a number of steps to solve a root-finding problem. This takes additional time compared to not it. The advantage though is that the entropy filter is significantly more robust and does not have the same issue with tunable parameters that artificial viscosity does. In many situations the entropy filter won’t be active, however, in flows that contain lots of shocks or are under-resolved, the entropy filter will be more active and this has a computational cost.

As Freddie says the entropy filter does not support adaptive time-stepping or implicit time schemes.

As to dimensionless values, there are loads of similar posts asking about this, I would recommend reading those. But the short answer is yes.

Finally, the time scheme I use generally depends on what I’m doing. Sometimes it’s handy to initialise a calculation with Euler as its really robust, but then for the calculation itself I would normally use either RK34 or TVD-RK, the CFL constraint of TVD RK is lower but you get some additional SSP properties that can be handy for highly non-linear flows.