Coordinate cut c-grid and dummy cells

zonexo

hello,

I've generated an airfoil c-grid. hence, the grid is folded until it touches itself. this is an artificial boundary, not a physical one.

however, i'm not sure how to form the LHS matrix because in the matrix, there are supposed to be no cells above or below the edge cells.

i've read a book which recommends using dummy/ghost cells. however, if i'm using dummy cells, will i be solving the system of eqns in NXN (original) or (N+1)*(N+1) (include dummy cells)?

Is that any other way? thanks!