[ALVRM]

I have built a pressure projection FVM solver for incompressible flow, and it works as intended if I use a small gravitational force, like 0.01 * 9.81. But when I use a larger value, like the actual acceleration of gravity of 9.81, the solver becomes very unstable and blows up.

I built the code without any third part libraries, so my question is conceptual... I would like to know what stability condition I am missing... My code is fully implicit for both the advection and diffusion term. I was using Crank Nicolson semi-implicit but realized that fully implicit is more stable.

I tried a pressure correction approach and it still failed at 9.81 source value. I might try to damp the pressure corrector, as I think that the large source term is causing the pressure to over correct and leading to large errors.

Any suggestions would be helpful. My ultimate goal is to create an unconditionally stable incompressible solver for natural convection.