Dear sirs,

I am using a primitive variable FEM NS solver. The problem is that i am puzzled over the outflow boundary conditions. Can anyone help me?

(1). Is this FEM NS solver giving you problems? (2). Is the outflow boundary conditions of the code giving you problems? (3). What is the outflow boundary conditions of the problem you are trying to solve? (4).If you are using a commercial code, all you need to do is to select the type of the outflow boundary conidtions and then supply the necessary information. (5). In most cases, there is not much you can do in the outflow boundary conditions. So, what is the fluid dynamic problem you are trying to solve with this FEM NS solver?

Hi. There are two books that i suggest you to read. [1]C. Taylor and T. G. Hughes, Finite Element Programming of the Navier-Stokes Equations, Pineridge Press [2]J. N. Reddy, An Introduction to the Finite Element Method, Mc. Graw Hill.

I think that the first one is exactly what you are looking for. All the book is about the discretization development of Navier-Stokes with primitive variables, and shows how to treat boundary condictions. The second one is more general book, but in the last chapters there is a brief presentation of Navier-Stokes with primitive variables discretization and boundary condictions treatment. If you are using some commercial software, so it´s more simple. Is just take a good look in the manual and follow all instructions to apply boundary condictions. In general ways, most FEM softwares if you don´t explicit the boundary condiction (Dirichlet type) the method by default assume null derivative boundary condictions(Newton type).

Good luck

Carlos Vilela

Hello there,

I am trying to resolve the Kerman vortex street shed behind a cylinder on average Re values. So the main thing is the outflow boundary conditions. I am using Flotran and phoenics and a code of mine in c++. The manuals at some point state that at the boundary you can put pressure to zero but i don't think that this is appropriate. In essence proper bcs should allow the vortexes to pass through without reflecting anything back to the flow. I know that this is a complex problem but some guidelines would be nice.

Thanks a lot Achilleas Tsompanos

Hi Achilleas,

if you want non-reflecting boundary conditions, then the problem is not what are the boundary conditions (e.g. given the variables or their derivatives) but rather how you do implement the boundary conditions. To avoid numerically reflective boundary conditions, you need to impose the boundary conditions using the method of the characteristics. THe characteristics of the flow are the quantities that actually propagate in the flow thourhg the boundaries (they are the eigenvector of the linearized, homogeneous problem). At each boundary there are characteristics that are incoming (entering the flow) and characteristics that are ougoing (exiting the flow). Idealy, you impose the boundary conditions (given physical quantities) on the incoming characteristics, while the outgoing characteristics takes values from inside the computational domain (you might need to extraoplate these). THe outgoing characteristics are carrying information outside the computational domain, while the incoming characteristics are carrying information inside into the computational domain. Therefore, sometimes it is enough just to set the incoming characteristics to zero, to avoid reflection. Once, this is done, one uses the values of the characteristics at the boundary to caculate the values of the primitive variables. And it is these values that are then imposed on the primitive variables. So the values that are eventually imposed on the primitive variables are a combination of incoming and outgoing characteristics.

I am not quite sure about your sofware if it has such a possibility.

Have a look at

Abarbanel et al. 1991, J. Fluid Mech. vol. 225, p. 557,

for the treatment of non-reflective boundary conditions in the simulations of the flow past a circular cylinder.

Have also a look at the review paper:

Givoli, 1991, J. Comput. PHys, vol. 94, p.1,

for a review of transmitting and non-reflective boundary conditions.

PG

you are quite correct the boundary conditions should be of the nonreflecting outflow/inflow type (because the flow is reversed in some areas your bc subroutine should be able to detect inflow and implement the appropriate conditions) in addition to other references given by Mr. Godon you might wish to read Kevin Thompson's paper in the Journal of Computational Physics vol 89 pp. 439-461 (1990) as well as Poinsot and Lele in J. Comp. Phys. vol 101 pp. 104-129(1992). both of these papers together will show you how to implement non-reflecting bc among others.

however, these papers assume you are using an unsteady formulation (time iterative scheme) if you are using a pressure based method you'll have to look somewhere else. i don't know if nonreflecting bc can be implemented in these codes you'd have to find out from someone who is more familiar with these schemes than i am. i know flotran is pressure based so you'll probably not be able to do it there. i have used flotran and i can't recall there being a nonreflecting bc available. the lack of nonreflecting bc is the Achilles' heel of pressure based codes (i couldn't resist). if pheonics and your code are also pressure based you'll have the same problem. if they are time iterative then you should be able to follow the procedure of thompson and poinsot and lele to apply the bc.

(Nearly ) ALL ABOUT OUTFLOW BOUNDARY CONDITIONS ...and MUCH MORE.. is in my new 1000+ page book, "INCOMPRESSIBLE FLOW AND THE FINITE ELEMENT METHOD", John Wiley (1999); with a new (2000) paperback edition to appear in 2 months