gradient calculation in ghost cell for the cell-centered finite volume method
 

Hi,
The compressible Navier-Stokes equations are solved on unstructured triangular mesh using a cell-centered finite volume method. In viscous fluxes discretization, the first derivative of velocity component at mid-point of each cell edge must be evaluated. For edge inside computational domain (not on boundary), the first derivative can be calculated using gradients of velocity at left and right cell centers which share the edge.
On physical boundary, ghost cells are created to implement boundary conditions. Flow variable values in these ghost cells are assigned according to specific boundary condition.
For a cell inside the computational domain, the gradient of a variable at the cell center can be calculated easily.

My question is:
How can we calculate the gradient in a ghost cell which is needed for evaluating the first derivative of velocity on the mid-point of edge which is on the physical boundary? The ghost cell has only one neighboring cell which is located inside the computational domain.

It will greatly appreciated if someone can answer my question.
Thank you

In general I wouldn't recommend using a reconstructed gradient on boundary faces to compute diffusion terms because it won't necessarily satisfy the diffusion flux implied by your boundary conditions. See the following reference about gradient reconstruction:

Betchen, L. J., Straatman, A. G., "An accurate gradient and Hessian reconstruction method for cell-centered finite-volume discretizations on unstructured grids," Int. J. Numerical Methods in Fluids, 62(9), 945-962, 2009.

This is one of my papers that might also be helpful:

C.T. DeGroot and A.G. Straatman, A Finite-volume Model for Fluid Flow and Nonequilibrium Heat Transfer in Conjugate Fluid-Porous Domains Using General Unstructured Grids, Numer. Heat Transf. B-Fund., vol. 60, pp. 252–277, 2011.

Equation 37 in the paper above can be used at boundaries for your diffusion terms and does not involve the boundary gradient. If you don't have access to that paper and are interested let me know and I can send a pdf offprint.

Hope this helps.

Can you please send me a PDF format for the referenced paper:

C.T. DeGroot and A.G. Straatman, A Finite-volume Model for Fluid Flow and Nonequilibrium Heat Transfer in Conjugate Fluid-Porous Domains Using General Unstructured Grids, Numer. Heat Transf. B-Fund., vol. 60, pp. 252–277, 2011.


Thanks.

Sure, message me your email.

Please send to mosawe@gmail.com. Thanks for the very quick response...much appreciated.