How is PyFR used for hypersonic simulations?

Hello everyone, I am gradually getting the hang of PyFR, and I would like to know how PyFR can be applied to hypersonic simulations. In such scenarios, the air is extremely thin, and the objects have very high Mach numbers, which is quite different from conventional CFD simulations. Has PyFR been successfully used in such cases before, and are there any relevant literature references I can consult?

My queries are focused on the settings of:

  1. solver-time-integrator
  2. solver-interfaces
  3. Boundary Conditions

My key settings are as follows:

[solver-time-integrator]
formulation = std
scheme = rk34
controller = pi
tstart = 0.0
tend = 0.01
dt = 1E-5
atol = 1E-7
rtol = 1E-7
errest-norm = l2
safety-fact = 0.9
min-fact = 0.3
max-fact = 2.5

[solver-interfaces]
riemann-solver = hllc
ldg-beta = 0.5
ldg-tau = 0.1

[soln-bcs-xmax]
type = char-riem-inv
rho = 0.00102688
u = 0
v = 0
w = -1978.794
p = 79.7791

No matter how I modify the parameters, the simulation runs, but I always encounter “minimum sized time step rejected.” I used the dtstat plugin for inspection and found that the time step is continuously rejected until it reaches a very small value, such as on the order of 1E-11, before it is accepted. Then, after a few steps, “minimum sized time step rejected” occurs again.

Why is this happening? Do you have any suggestions? Any help would be greatly appreciated.
Sincerely,

Given that this case has a Mach number greater than 1, you will probably encounter shockwaves/discontinuities. The standard FR method cannot approximate these features without help, so you should turn on the entropy filtering. However, you must disable the adaptive time stepping as this is incompatible with entropy filtering.

Also, how confident are you that the Navier-Stokes equations are valid in this regime?