I am trying to simulate a - what I thought - rather simple test-problem. Consider a closed container, the lower half filled with water, the upper half with air. Gravity is acting downward. No walls are moving, so you would expect this configuration to be steady. Any simulation should give you zero velocities, nearly constant pressure in air and (with depth) increasing pressure in water.

Using a standard finite-element Galerkin method (Taylor- Hood triangle) in combination with the VOF-approach (linear approximation of density and viscosity, both fluids simulated), I found this problem can *not* be handled. During the first timesteps the velocities remain zero and the pressure solution is exact. Later the surface becomes unsteady and with increasing velocities the simulation "explodes".

Simulating the same problem without gravity results in no problems. The code without VOF has been validated in lots of problems including gravity-related ones. Computing other problems with the VOF-approach without gravity gives again no problems. The VOF-function is approximated by a linear function within the triangle.

Summing up I wonder whether there is some bug in my code or if this is some other (deeper) problem related to the linear VOF-approximation in combination with finite elements.

Does anyone have similar problems - or (even better) could hint at some inconsistency with the above approach ?

Any ideas are welcome ...

Thanks, Chris

I am no expert in VOF, but it sounded like that when you turn on the gravity, the water is on the top and the air is on the bottom. Change the direction of your gravitational field to see whether your bugs are still there.

Thanks for responding John. This was of course one of the first things I tested when I first saw the problem. Unfortunately the whatever-it-is-problem lies somewhat deeper.