I am solving the conservation form of the Euler equations using cell-centered finite volume method.

U + dF/dx + dG/dy = 0

At the wall boundaries I set the derivative of the flux to zero i.e dF/dx = 0 |y = wall. However the cell centered velocity for the node adjacent to the wall does not approach zero despite uniform grid refinement. Why is that?

Shuo

zero flux does not mean zero velocity. zero flux basically means no different in velocity accross the wall boundary. you may want to try a no-slip boundary instead.

no slip boundary u_i = - u_i-1

that way, you can ensure that velocity AT the boundary is zero, and hence the velocity near the boundary will approach 0.

I did that for the fluxes.

i.e for

dU/dt_(i, j) = -1/delta_x(F_(i+0.5, j) - F_(i-0.5, j)) - 1/delta_y(G_(i, j + 0.5) - G_(i, j - 0.5))

at wall | (i + 0.5, j)

F_(i+0.5, j) =

[ 0 P_(i - 0.5, j) //boundary condition 0 0 ]

G_(i, j + 0.5) =

// stays the same

[rho_(i, j+0.5)*v_(i, j+0.5) rho_(i, j+0.5)*u_(i, j+0.5)*v_(i, j+0.5) rho_(i, j+0.5)*v_(i, j+0.5)*v_(i, j+0.5) + P_(i, j+0.5) (e_(i, j+0.5) + P_(i, j+0.5))*v_(i, j+0.5) ]

Since you solve Euler (rather NS) equations, there is slip at walls, so you should not expect zero velocity near the wall.

no....not for the fluxes...just create a layer of dummy cells along the boundary and change the direction (reverse by 180 degrees) for the NORMAL component at that point in dummy cell. Keep rest things same.viz. in c:

for(i=1;i<=nx;i++)

{

mirror_dp[i]=dp[i][1];

mirror_pp[i]=pp[i][1];

mirror_up[i]=up[i][1];

mirror_vp[i]=-vp[i][1];

mirror_ep[i]=ep[i][1];

mirror_ap[i]=ap[i][1];

//printf("\n%lf %lf %lf %lf %lf %lf",dp[i][4],pp[i][4],up[i][4],vp[i][1],ap[i][1],ep[i][1]);

} Also, for cell centered, as the information is stored at the cell center AND NOT AT THE WALL ITSELF, it might be one of the reasons not to get zero velocity at the wall.mail me at a.patil@iitg.ernet.in if reqd.

i am modelling a supersonic impinging jet and the problems occurs for across wall jet. i have about 40- 50 grid points across this jet. Is this enough resolution?

Shuo

For the concept of "dummy cells", I recommend you "computational fluid dynamics: principles and applications" written by J. Blazek, 2nd edition. It help you understand the implementation of boundary conditions.