wall b.c. in presence of gravity
 

in my cell-centered fvm code, the pressure in the ghost cell is set to the pressure in the boundary cell - however, if gravitational force is taken into account then:

p_ghost = p_bndry + r_bndry*grav*dy

dy = y_bndry - y_ghost

but now p_r (i.e., p_ghost) is not equal to p_l (i.e., p_bndry) in the riemann problem. the solution looks fine but mass and energy are not conserved. and setting p_ghost = p_bndry does not work either.

has anyone encountered such a problem - any help in setting wall boundary conditions in the presence of gravity will be greatly appreciated. thank you.