transient term treatment

Mike

I have difficulty in the calculation of velocity and pressure fields for the transient flow. I am using the SIMPLE method to solve the velocity and pressure field for compressible flow. When the density is only function of pressure (isothermal) there is no problem, while when I solve the energy equation and the density is function of both pressure and temperature I get negative pressures. In a general form for the transient term in the countinuity I write:

d/dt (rho)=d/dP (rho) . dP/dt+ d/dT (rho). dT/dt

Now for ideal gas we have: rho=P/(kT)

d/dP (rho)= 1/(kT) (k is molar gas constant)

d/dT (rho)= -P/(kT^2)

The flow is laminar and the mach number is very small, however the density variation is big. Is there any trick to handle the transient part in the pressure equation?

Thanks for the help.