Hi

I am simulating a free jet using Euler equations in the r-z plane. What are the boundary conditions for the symmetry plane and how do I implement it numerically?

Cheers Shuo

No mass flow across the Z axis.

what about the density and pressure?

No jumps, there is no mass crossing the symmetry plane, also be carefull, no mass crossing means the normal component of the velocity vector is equal to zero, but the parallel componet is not. you can check the Peric or the Versteeg & Malalasekra books for full details. Good Luck.

If I understood correctly you are using cylindrical symmetry. Write the equations in r-z-theta coordinates and set all theta-derivatives and theta-velocity to zero. You will get an equation that looks almost like the 2-d equations but with some source terms.

It is similar to the rigid wall boundary condition.

So its something like:

v_0 = 0

u_0 = u_1

P_0 = P_1

rho_0 = rho_1

where u & v are the velocity components in the z and r directions respectively. 0 is the symmetry boundary and 1 is the nearest node.

Shuo

In my case where flow is axi-symmetric, I set like that. The implementation of axi-symmetric flows is very straightforward. The results of my axi-symmetric cases were right compared to the analyric solution or experimental data. Good luck!