Subsonic or transonic flow over a bump in a channel.
 

For these case, we prescribe stagnation pressure and temperature at subsonic inlet (physical BC). Now we extrapolate velocity from inside the solution domain (numerical BC). For calculating internal energy (e) for solving energy equation for in-viscid flow, we require velocity values. Therefore does stagnation properties means these value of velocity at inlet will be zero ?
Numerically, we would get some velocity by extrapolation.
What is the physical meaning of taking stagnation properties at inlet?


My code is using MacCormack scheme using Artificial Viscosity apporach in 3D for euler Equation. I am getting for M=0.7 a distorted result. I have attached my result below and the standard result given in Hirsch book. Can any one please tell what I may be doing wrong?

Stagnation properties at inlet means, static quantities and velocity would adjust to keep stagnation quantity constant. All you need is 5 variables 3 velocity and two thermodynamic quantities. Calculate static pressure and temperature from stagnation values and extrapolated velocity. With these five quantities you can calculate any other variable in Euler equation.

Thank you for your reply. I did the same and I am getting good but not so accurate result. To know Mach Number, I needed sonic velocity at the inlet. For this I needed temperature or P and rho at inlet. Since, we have only stagnation information, I used these value of previous time-step at inlet. Is it correct, or their is any other better method?

Can you please suggest some reference to validate M=0.7 flow over bump, with plot for Cp over the lower wall?

Thank you.