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BC for a reservoir discharge problem

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Old   May 25, 2009, 15:12
Default BC for a reservoir discharge problem
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I have been trying to solve such a problem: A pipe contains high-pressure and -temperature gas and is connected to two low-pressure reservervoirs. At first, both of the pipe ends are closed, then the left end is open, and the gas exhausts into the left reservoir with an expansion wave traveling rightward into the pipe. After the pressure near the right end becomes lower than the pressure in the right reservoir, the right end is open, and the air flows from the right reservoir into the pipe.

Now I ran into a problem of the BCs on the open ends. My current BCs are:
on the left boundary: P1 = P_left(pressure in the left reservoir = 1 bar), T1 = 2*T2-T3, u1 = 2*u2-u3(extrapolation from Anderson's CFD book);
on the closed right boundary: P(n) = 2*P(n-1)-P(n-2), u(n) = 0, T(n) = T(n-1)(adiabatic);
on the open right boundary:P(n) = P_right(pressure in the right reservoir = 1.5 bar), T(n) = T_right = 300 K, u(n) = 2*u(n-1)-u(n-2);
I used MacCormack scheme to solve this problem.

The result when the left end is open and the right end is closed is shown in the first attachment, and the final steady-state result in the second one. Now I am confused about why there is a kink in the pressure plot at the left outlet. I expect the pressure is equal to the left reservoir pressure which is 1 bar.

I think my BCs are not suitable for this problem. Does anyone know any better BCs?

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Old   May 26, 2009, 10:10
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You can employ characteristic boundary condition for the problem.
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