[Fahraynk]

Hi, I'm trying to solve a basic problem with finite difference method in 2D.

I am modeling a pressure wave moving from right to left in a 2D domain. The solution seems fine until the wave hits the right boundary. Then, a pressure gradient develops and the velocity from right to left starts to increase.

I have a square grid and set the left side boundary overpressure to 20K Pascals, and temperature to be 356.79 Kelvins.

All other boundary conditions on all walls are outflow conditions. They are calculated based on a calculated slope of their adjacent points.

Initial temperature is 298 [K].

Initially, a pressure wave travels from the left wall to the right wall. The wave travels as expected, raising the pressure as it goes.

The problem is after the wave hits the right outflow boundary. If time keeps incrementing, the pressure falls on the right hand side and I get a pressure gradient.

The gradient looks like this from right to left for one row of grid at time = 0.10:

121055.9
120744.7
120433.5
120122.4
119811.2
119500.1
119188.9
118877.7
118566.6
118255.4
117944.2
117633.1
117321.9
117010.8
116699.6
116388.4
116077.3
115766.1
115455.0

My question is... is this gradient normal? I thought the pressure would reach a steady state after the wave passes. While troubleshooting, I noticed the velocity seems to keep increasing long after the wave passes, and there is no velocity gradient. I suppose this increase is due to the pressure gradient. The temperature and internal energy show a similar gradient. Density stays approximately constant.

Any help appreciated. Should it reach steady state right after the wave passes?

[FMDenaro]

Originally Posted by Fahraynk

All other boundary conditions on all walls are outflow conditions.

Wall or outflow? How many outflow sections?


However, for compressible flows you have to set properly the boundary conditions depending on the subsonic/supersonic conditions. That happens to take into account the direction of the characteristic curves.


See https://www.google.com/url?sa=t&rct=...J-tLsyDnGaxapa

[Fahraynk]

Originally Posted by FMDenaro

Wall or outflow? How many outflow sections?


However, for compressible flows you have to set properly the boundary conditions depending on the subsonic/supersonic conditions. That happens to take into account the direction of the characteristic curves.


See https://www.google.com/url?sa=t&rct=...J-tLsyDnGaxapa

Hi, thank you for the reply. I set everything to outflow, no walls. The only thing I did not set to outflow are the pressure and temperature on the left side boundary.

Thanks for the paper, I will read through it.

[Fahraynk]

Edit : I forgot a vector square is a dot product, please ignore (can't figure out how to delete this reply)

[FMDenaro]

Originally Posted by Fahraynk

In this paper, they outline the non-conservation form in summation notation.

In equation 4 of the paper, are they saying the (e + V^2/2) term in the energy equation is written out (e + (p/2) (u^2 + v^2 + w^2)) ? (where V is vector of velocity [u, v, w] and e is internal energy)

Is that valid? Or am I wrong? Because in the energy equation as I have seen it, V is a vector, so the energy equation would really be three equations?

(uk uk) is just (u^2+v^2+w^2) (kinetic energy) that sum to the internal energy to provide the total energy E

[Fahraynk]

Hi, after reading through the paper you graciously posted, I am stuck.

I'm trying to figure out on a boundary when I can't use the interior flow-field. ( is velocity in direction). I can't use the interior flow field, per the paper, because this represents an incoming wave.

The paper mentions something about solving 1D Euler to get this variable, but I'm not sure how to translate a 1D solution into .

comes from solving 2D subsonic inflow on one boundary. The paper states I need 4 conditions for a 3D boundary, so I assume 3 conditions for a 2D boundary. (Is that a valid assumption?) I choose pressure, density, and internal energy (P, p, e) to be constants on this boundary.

Then, I reduce the system to two equations on the boundary by following guidelines in the paper :



But I can't time step for the boundary condition until I figure out .

Any help is greatly appreciated!

Originally Posted by FMDenaro

Wall or outflow? How many outflow sections?


However, for compressible flows you have to set properly the boundary conditions depending on the subsonic/supersonic conditions. That happens to take into account the direction of the characteristic curves.


See https://www.google.com/url?sa=t&rct=...J-tLsyDnGaxapa