dear

i have a question about the period boundary conditions, when i compute a square duct with solving 3d compressible NS equations. as you known, the energy will decrease along the streamwise because of friction. but when i set the period BC, the density rou, the u, v, w, and p will be set equate between i=min and i=max, is it right? if i set it, it means that the energy will be constant. this confused me. by the way, i compute the square duct with Re=4800 and Ma=0.5. if i do not use the period BC, how set the inflow condition? best regards

In the streamwise direction, you have to specify both pressure drop and temperature drop - just take example of water flowing in the channel, the pressure can not be the same.

thanks for your responses let's consider 1d equation. at the n time step, the inflow pressure is p_n(i_min), the outflow is p_n(i_max). p_n(i_min) > p_n(i_max) because of viscous. at the n+1 time step, we set the p_n+1(i_min) = p_n(i_max), is it right? if yes, the inflow pressure will be decreased at every time step, so it will be small even negative after enough step? i known this is a mistake, but why ? yours sincerely Bin Li

Hi,

can you explain me the geometry of your problem, specifying inlet and outlet conditions? I can not understand the periodicity condition between inlet and outlet. Moreover, if no heat flux through the boundaries is allowed and the gravity force is not included, the averaged stagnation energy must be constant in the streamwise direction. Of course, mechanical energy is lost because of wall friction and viscosity.

Nicola

I don't think you can use periodic boundary conditions for your problem as stated. As you note, there will be a pressure drop along the section and periodic b.c. would result in multivalued pressure and density.

I can imagine using periodic b.c. if you had a nonconservative body force like an electromagnetic pump driving the flow, in which case the pressure gradient could be zero and so the inlet and outlet pressures would match.

You would not specify initial or inlet flow as the solution should evolve to fully-developed Poiseulle flow over time.