JunctionN pmix

[RaphaelGebhart]

In my opinion, there exists no unique split for the steady mass flow pressure phat and inertial pressure r at a
junction, i.e. the implemented mixing equation:
if not assumeConstantDensity then
p_mix = sum(w2.*p);
else
p_mix = sum(w.*p);
end if;

is just one choice, which however fullfills p[1] = p[2] <-> p_mix = p[1] <-> p_mix = p[2]. Note that any (weighted) mean with nonzero weights (e.g. arithmetic, geometric, harmonic) would fullfill this "requirement". In my opinion, without usage of the inertial pressures r_in[:] no mean can a priori be stated to be superior, therefore we might consider simplifying the pressure mixing equation to e.g:

p_mix = 1/N*sum(p)

Futhermore, we could add the possibility to use the inertial pressures r_in[:] by enhancing the mixing pressure with a first order filter:

p_mix_tilde = 1/N*sum(p);
T*der(r_mix_tilde) + r_mix_tilde = r_mix;
p_mix = p_mix_tilde + r_mix_tilde;

which can be interpreted as the most simple "volume"-like differential equation.