To impliment outlet boundary conditions which of the following equations is true: d2 phi/d x2 =0 or d phi/d x =0

And how to discretize d2 phi/ d x2 =0 in finite volume formulation

Ok I found out the answer. Setting the first derivatives of the variables u,v, and T or phi equal to zero at the exit plane is appropriate if the transverse velocity (v for example)is negligible at the boundary, which is not necessarily true for unsteady wakes exiting channels for example. Setting the second derivatives equal to zero at the exit is found to be more accurate but does not result n an unconditionally stable procedure and is not accurate as the wave boundary condition which reads: d phi/d t + c d pgi/ d x=0 The wave speed c is the mean channel inlet velocity Uo in case or horizontal channel or the average exit velocity in general.

Hi

Look at the AIAA paper - 84-1552, "Three Dimensional Unsteady Euler Equations Solution Using Flux Vector Splitting" by D.L. Whitfield and J.M. Janus.

They have derived characteristic variable boundary conditions for inflows and outflows and impermeable wall. It is simple and straightforward.

Ravi.

Dear Tamer,

Could you please explain more detail about How to descretise the wave boundary condition on FVM?

STN

How can I get such an old conference? D. L. Whitfield and J. M. Janus, "Three dimensional unsteady euler equations solutions using flux vector splitting," 17th Fluid Dynamics, Plasma Dynamics, and Lasers Conf., AIAA paper no. 84--1552, June 25--27, 1984.

Obviously, using zero second derivatives BC's is wrong. So is the wave boundary condition.

Why boundary conditions of second dervative not accurate?