Hello to all! In my code I use the pressure correction method to solve a compressible unsteady flow.At the inflow the velocity is prescribed.When I correct the pressure: P(i,j,k)=P(i,j,k)+a*P'(i,j,k) , I also correct the density: Density(i,j,k)=Density(i,j,k)+a*P(i,j,k)/R/T(i,j,k). But when I compute the density from the equation of state (density=Pressure/R/Ttemperature) I have totally different values.From the first method the density is about 1.5 kg/m^3 and from the equation of state is about 0.8 kg/m^3.Can you please tell me a safe way to compute density and the absolute pressure? Thank you in advance!!!

For compressible flow, the independent primitive variables are (rho,u,v,w,E), or (p,u.v,w,h). You can not use density=density +a*P/R/T if you already use (p,u,v,w,h) as independent variables.

I use the set (p,u,v,w,h).But how can I compute the density then.From the equation of state I find one value and from: density=density +a*P/R/T one other.I thought that these vakues should be the same.One more question:In incompressible flow,the pressure is corrected with this formula: P=P+a*(P'-P'reference).This should happen also in the compressible flow? Thank you

with (p,u,v,w,h), you have rho=EOS(p,h), but use density=density +a*P/R/T to update density is nonsense now. If your really wishes to update density by incremetal formula, then differentiate d rho= d EOS(p,h), you will find numerical difference between rho=EOS(p,h) and rho=rho+d EOS. In compressible flow, you need not use a P_ref. In incompressible flow, since it is gradient p not p that matters, adding any reference value to pressure does not matter. This value can be zero.

Hello again. Thank you for your response.My question is that I have read in many papers, that the proper way to correct density is with the formula: density=density+a*P/R/T. If this is not the proper,can you please tell me how to implement this. One more question.I prescribe the velocity in inflow.Can I also prescribe pressure,or is this too much? Thank you

I assume you are using low Mach number assumptions (otherwise no point in correcting Pressure, change model). If you are doing so, then what your thermodynamic pressure?, if you are using an open flow for examplem, then you assume ambient pressure. In this case the pressure you obtain in the pressure solver has NOTHING to do with thermodynamic pressure, therefore you do NOT have to correct the density. In fact you are probably adding 2/3div(u) to it to simplify the modelling of the viscous part.

When you correct the pressure (SIMPLE style algorithms), you are just enforcing the costrain D(rho)/Dt=0 (continuity equation). The tricky thing is, you need to model drho/dt which probably you do not know yet (before correcting pressure) so the coupling between rho,u,P is weak or very weak selon density gradients. If density gradients are moderate the pressure correction is far from good and your flow becomes nicely unstable. It seem a very simple thing but it is not.

If you have variable pressure, then there is place for the denisty corrections which you assume proportional to the pressure correction (cte T is one iteration) which gives an equation for P "similar" to incompressible flows (not in nature). see book by Ferziger and Peric.