Clarification on Non-Dimensionalization in Elixir Navier-Stokes Example

[teddyz1999]

Clarification on Non-Dimensionalization in Elixir Navier-Stokes Example

Hi,

I’m working on understanding the non-dimensionalization process for the Navier-Stokes equations in the example elixir_navierstokes_taylor_green_vortex, specifically the parameter mu = 6.25e-4, which corresponds to Re = 1600.

It appears that the viscosity mu is directly set as 1/Re . However, I would like to clarify the following:

1. What are the reference velocity (U_ref) and reference length (L_ref) used in the non-dimensionalization process?
2. How is the non-dimensionalization implemented in Trixi ?

A detailed explanation of how mu and Re relate to the non-dimensionalization choices in this context would be very helpful.

Thank you !

[knstmrd]

(Not a developer, but an active user; maybe someone will correct me): the end-user of Trixi is expected to take care of all the non-dimensionalization themselves and to ensure it is consistent. One could run Trixi even in non-scaled variables (but round-off errors might become an issue).
mu=6.25e-4 corresponds to Re=1600 in case rho_ref=1, U_ref=1, L_ref=1 (and in this example the domain is then of size 2pi x 2pi x 2pi [Length units]), which I assume is what is assumed in the example.

[JoshuaLampert]

See also #2095.

[teddyz1999]

From the viscous flux terms, I infer that this equation is not written in a non-dimensional form. The entire equation appears to be in a dimensional form. If it were in a non-dimensional form, there would at least be a Reynolds number present as a coefficient in front of the viscous flux terms.

[knstmrd]

But the Reynolds number can be incorporated into mu (at least that's what I did when doing some N-S stuff in Trixi a while ago, i.e. something along the lines of μ0 = 1.649951e-05; μ_ref = p_ref * t_ref; equations = CompressibleNavierStokesDiffusion2D(equations_euler, mu=μ0/μ_ref, Prandtl=Pr)
So one can have a potentially inconsistent scaling of the variables (even for the Euler equations), but that is on the user side