What are the conditions for this type of boundary in terms of rho, u, v and P? Can I just extrapolate the variables from witihin the domain assuming a subsonic outlet?

Shuo

It depends on the problem that you are looking at . For fluid flow problems it would be sufficient for most cases . But if you are interested in noise computation then you need special NRBC.

I am modelling a supersonic impinging jet. when I extrapolated all variables from the interior for the far field the wall jet along the plate was massive- much larger than the jet issued from the nozzle!!. The domain was 4D(x) * 2D (y).

How are you doing? I am also suffering from NRBC. To suppress unphysical reflection from edges, I have searched a good way to impose NRBC or infinite condition. In doing so, I found a good reference on NRBC.

See, section 15.4 in the book, 'computational fluid dynamics volume 2, fourth edition' written by Klaus A. Hoffmann and Steve T. Chiang. They well explained on NRBC and compared each others.

Based on their conclusion, the sponge layer(or absorbing layer) provides the cleanest solution with no reflected waves observed.

I just completed the one-dimensional code with the sponge layer. I am trying it to extend to multi-dimensions. If you concern this way, see that reference. It was good to me.

Another way of absorbing the outgoing waves is using grid stretching and filtering close to the domain boundaries. This computational cost of this method is lesser than the sponge layer approach.

Can I ask you about the way you mentioned above? I am feeling that the sponge layer approach is computationally expensive.

The simple idea of the method is as follows.

(i) Grid stretching transfers the energy to high frequency content

(ii) numerical filtering removes the high frequency component

This method is referred also as energy transfer and annihilation.You apply the grid stretching and filtering in the buffer zone.Because of the grid stretching the expense reduces.Point to note is that the method is ad-hoc and requires some testing.

Reference :

A General Buffer Zone-type Non-Reflecting Boundary Condition for Computational Aeroacoustics - N. Edgar and M. Visbal AIAA-2003-3300 9th AIAA/CEAS Aeroacoustics Conference and Exhibit, Hilton Head, South Carolina, May 12-14, 2003

Can I ask you again about your recommendation? Throughout my resource, I could not find that paper. If you have that paper in pdf format, could you send it for me? I am really hoping to reduce computational cost required in the sponge layer approach. It was tough to run.

What is your e-mail address ? . I used this method when I was studying the computation of aeroacoustic noise due to vortex shedding from a cylinder. I started with the sponge layer and it was too expensive compared to the size of my domain and hence I moved to this method. I used a grid stretching of the form dx=1.2 dx in the buffer zone and used a 10th order filter of visbal and gaitonde(2001) with the coefficient of the filter set to 0.3. As far as the number of points I used 25-40% of the number used with the sponge layer case.

My email address is jwpark1@gmail.com. I really appreciate your kind advice. But I am wondering that it is also applicable to the Euler equation. As you mentioned, you used that method for aeroacoustic problems. Anyway, if you do not mind, I would like to ask you the paper through email.

Thanks in advance.

I applied it for both Navier-Stokes and Euler equations . In aeroacoustics for the noise part Linearized Euler equation is often used.

As I requested, can you send the paper to me? My email address is jwpark1@gmail.com