Hi there,

I am currently writing a 3D unsteady Navier-Stokes solver using the FVM and Lax-Wendroff scheme (1 step) for the time integration. I have a problem to implement the no-slip BC's, at least to correct the viscous flux. The algorithm is the type of node-based so that I have the state variables stored in the nodes of each cells. The shear stress is then evaluate in the mid-cell edges and contribute to each surrounding nodes. Concerning the wall boundary treatment, I put a dummy cell row inside the wall where each nodes contains a negative velocity corresponding to the real one inside the real flow domain. This dummy cell row contribute to the correction of fluxes for the next time step state values in the vertex nodes of the cells attach to the wall. When the code is run, the divergence appears quite quickly. Actually, It is seen that there is oscillation of pressure then velocity at the wall (like odd-even case ...) Has anyone of you an idea why I am facing this problem (I have already a numerical smoothing) and also how handle the wall BC's with the method I use.

Cheers.

hi there,

I guess that you are using a collocated grid arrangement! If that's the case, to avoid some pressure velocity decorolation you must use the Rhie-Chow model. Rhie, C.M. and Chow, W.L. "A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation." AIAA Journal, Vol 21, 1983, pp 1525-1532.

If you are actually using this model, well i'm sure that you could find some very useful, and clearly explained, information in this following paper: Morinishi, Lund, Vasilyev and Moin "Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow." J. Comp. Phys 143, 90-124, 1998.

You can download this paper on-line at the following address: http://mae.uta.edu/~lund/

I hope this helps. Sincerely,

Frederic Felten CFD Laboratory UT Arlington. http://utacfdb.uta.edu/~felten/

You seem to have different problems with your solver, the non-divergence of the velocity field and the odd-even spatial oscillations.

The odd-even oscillation of pressure and velocity are due to their mutual decoupling. If even order discretizations are used to compute both the source term of the Poisson equation and the pressure gradient term(s) in the momentum equation(s), then the velocity and pressure at a given point are insensitive to each other (i.e., do not depend on each other). So you need to use some kind of biased (odd-order) discretization for one of these terms. This is a standard practice when using non-staggered (collocated) grids. Rhie and Chow method can be used but a more recent method by Zang et al. (Journal of Comp. Phys., 1994) might be more helpful. One of the other authors is Prof. Street from Stanford Univ.

Even with oscillations, you still should have a divergence free (but incorrect) velocity field when using non-staggered grids. Divergence becomes non-zero eventually after the oscillation have grown significantly in amplitude. You were saying that the divergence starts appearing close to the wall which suggests that your pressure BC is not accurate. Spatial oscillations in the wall normal velocity component are produced if an appropriate BC is not used. See Gresho (Annual Review of Fluid Mech., year = 199?) for details.

Here is a possible source of error at the walls. For each boundary cell, you have ghost cell. The velocity components in the ghost cell are negative of the components in the boundary cell, the cell face (i.e., the wall) has zero velocity and hence there is not convective flux. However, this works only for Euler flows. In incompressible viscous flows, velocity divergence condition demands that the wall normal component of velocity has zero gradient along the wall normal.

If your wall is aligned to the x-z plane then,

dv/dy = 0 at the wall (i.e. the cell face where you compute the viscous flux). So there is no normal viscous stress at the wall.

For this condition to be valid on the wall, v(ghost cell) = v(boundary cell). So you have to enforce this condition while computing viscous stresses. If you use the condition v(ghost cell) = -v(boundary cell) that is required for the no-slip condition, you create non-zero dv/dy and the near wall flow will not be accurate.

Hi Kalyan,

A small correction. The method of Zang, Street, and Koseff is the same as the Rhie-Chow method as far as the elimination of p-v decoupling is concerned!

chidu...

je suis un chercheur marocain dans le domaine CFD hydraulic option les ecoulements a surface libre je cherche des articles ou livres qui parlent de la modelisation mathematique et numerique des écoulements surfaciques merci

Pour obtenir de l'aide, je vous suggere de poster a nouveau votre message. Mais comme un nouveau message (presentement il est vu comme une reponse a une autre question). De plus, je crois qu'il serait preferable de le faire en englais. Vous pourrez ainsi rejoindre un plus grand nombre de chercheurs.

Bonne Chance.

>For this condition to be valid on the wall, v(ghost >cell) = v(boundary cell). So you have to enforce this >condition while computing viscous stresses. If you
:use the condition v(ghost cell) = -v(boundary cell)
:that is required for the no-slip condition, you
:create non-zero dv/dy and the near wall flow will not
:be accurate.

I have never been able to stomach this image method on bounded domains...I can see that it is OK when the wall is infinite in the tangential directions, but I cannot see an image w.r.t. the wall of a (say) rectangular domain.

Can anyone shed some light ?

Best, Peter