[coagmento]

I would like to know whether upwind donor cell scheme is appropriate for solving the 2D continuity equation
,
where u and v are horizontal and vertical velocities, respectively.

I assume that u and v vary spatially on (x,y).
I do not assume that the fluid is incompressible.

Is the donor cell still appropriate even when the velocities are spatially varying?

[FMDenaro]

Originally Posted by coagmento

I would like to know whether upwind donor cell scheme is appropriate for solving the 2D continuity equation
,
where u and v are horizontal and vertical velocities, respectively.

I assume that u and v vary spatially on (x,y).
I do not assume that the fluid is incompressible.

Is the donor cell still appropriate even when the velocities are spatially varying?

yes, just take the local sign of the velocities...
be only careful in the stability constraint that require the treshold on the maximum velocity