pressure inlet LODI BC for Euler eqn

DSS

Hi,

I need to apply the inlet boundary condition based on LODI formulation by Poinsot and Lele. I had successfully implemented the velocity inlet, in which you need to find d(Rho)/dt in terms of other quantities, and pressure is obtained from the specified inlet temperature.

In the case of pressure boundary condition (temperature and total pressure are specified), when I try to formulate, I end up in having couple of equations with respect to d(Rho)/dt and d(U)/dt. Can anyone help me in formulating this boundary condition?

Thanks in advance, Shyam