Interpolation for ghost cell help

zonexo

hi,

i am trying to use interpolation to get the pressure value of the ghost cell. I have dp/dn=0 at a location (boundary) and a few other pressure values at the neighbouring nodes.

my method is to use linear interpolation where p=a0+a1*x+a2*x2 at 2 neighbouring nodes. to use the dp/dn=0 condition, i differentiate the eqn to give dp/dn=a1*dx/dn+a2*dy/dn. a 3X3 matrix is formed and its inverse is computed to get a0,a1 and a2. Similar method can be used for bilinear and quadratic interpolation.

however, the problem is that the matrix can be singular at times.

Is there a better interpolation method which makes use of these conditions and yet it is stable?

Thank you!