Hello!

I'm using the conservative formulation programming my own code in Matlab, in order to solve a supersonic flow over a body. I'm using unsteady Euler equations and an aproximation time-dependent. But my question is How can I implement the bundary condition v*n=0 at the body surface?. Remember I'm using conservative formulation.

Thanks.

Hi!

For supersonic formulation the Euler Equation is not good. Try the N-S formulation with the any turbulence model. This is necessary to a good convergence process. With Euler, in the surface, the velocity is zero, ok! You must attribute this value to all control volume locate in the wall.

Takachi

If you haven't unknows on the body surface (like cell-centered formulation), one choice is to impose that the flux through your surface segment reduce to the pressure contribution, i.e.

Flux_normal_wall = [0 p*n_x p*n_y 0]^T

where n_x and n_y are components of the normal to the surface. p is the pressure extrapolated on the surface (with the method of your choice). It works rather well.

Hope this help

JF

Hi "doctor" Blade, before I can answer your question, I need to know the kind of spatial discretization that is being used (finite element with strong or weak formulation, cell centered FVM, vertex based FVM,...).

Thanks for your answers. JF, I do not understand why flux on the surface must be balanced with pressure.

Hi, Takachi, but I am going to keep the Euler formulation. I'm not an expert in CFD, so I think complete N-S formulation would be more difficult.

Hi, Seb, I'm seeking for solving with a finite difference method. (I think that Mac'Cormack steps in time would be sufficient). I'm using an structured elliptic grid, which external boundary is a circle of 10 times the characteristic body lenght. I'm going to try to explain all of you my method, in order to know your opinion.

i) I would start with some flow solution, rather arbitrarily. I would yield the freestream conditions on the external boundary in all instants of time.

ii) I advance with time steps of Mac'Cormack's algorithm, in order to be able to solve the transonic, subsonic and supersonic field that will be originated. But the problem I have is in the internal boundary condition.

What do you think?, Do you believe I'm going to be alive when I reach the convergence?.

If you are using a finite-difference approach then the standard method is to compute the tangential velocity at the point adjacent to the boundary and project that to the boundary. Set the normal component to zero, and then transform those components to Cartesian or whatever coordinate system you are using.

You should be able to get convergence rather quickly. Depends on how many bugs you will have in the code though...

I would use a "ghost-point" approach on the surface, ie. create an additional point inside the body. Then set the normal velocity (call it V) to zero by setting V(J-1) = -V(J+1) where J is the surface. Works well as long as your grid is sufficiently fine so that the ghost point is as far from the surface as the point inside the flow is. Use a similar approach for other variables, and you can actually solve the equations on the surface as well.

-- Jarmo

Hi Blade, Jarmo and Ag have given good enough info on the good approach on the implementation of the BC.

But in the order to solve your problem and get to convergence, you will also need a descent artificial dissipation scheme (Leer, QUICK,....).

Talking about this...

Does anybody know some website or paper in which I could see an example of procedure of this kind of simulation?.

I'm not searching for an advanced method, but one simple (e.g. Maccormack's).

Why not using Jameson's FVM, developed in the 80's? It is simple, well docummented and addresses the wall BC you asked about originally. You may find it in most textbooks, or go to the original papers (e.g., A. Jameson, Solution of the Euler Equations by a Multigrid Method, Appl. Math. Comput., vol. 13, pp. 327-356, 1983).

It is about NORMAL velocity=0 (not a problem for Euler). Not TANGENTIAL velocity=0.

Depending on the spatial order of your numerical schema you can use 1 or 2 mirror cells. Worked fine for me

does FVM mean Finite Volume Method?. If so, I have no idea of FVM at all. I only know something about Finite Differences.

You know, the beginning is a hard time...

FVM indeed stands for Finite Volume Method. It is much simpler than you seem to imagine. I still suggest you to read the references I recommended or other introductory textbooks to CFD (e.g. Patankar or Ferziger & Peric).

OK!

I´ll send to you the formulae about the wall boundary conditions.

My messenger is: takachi_e0028@hotmail.com

Wait my e-mail.

Regards,

Takachi

I've sent you an e-mail to both directions, telling you to write me to this other e-mail (see above).

thanks.

sir,

i need to know how to compute fluxes for wall boundary conditions,inflow,outflow,far-field boundary. i'm using van leer fvs cell-centred fvm for my scheme.

Sorry, I've not used never FVM. But If I can help you, you must elaborate your question a little bit.