Fast simulation of viscous compressible droplets

Tom Holden

Hi,

I need to simulate droplets of a compressible viscous substance moving under the influence of a vector field of forces (e.g. gravity).

Now I need to be able to perform around 1000-10000 timesteps per second (not all on the same particle) on a standard PC, thus I presume I have to make some fairly heavy simplifications.

Any suggestions for these simplifications would be greatly appreciated.

My current idea was to basically "rederive" the Navier Stokes equations for (linearly interpolated) triangles arranged in a circular fan (with vertices on the droplet edge and one central one), and then use cubic hermite interpolation for the droplet outline, trying to minimise the error in the Stress Balance Equation.

Three things worry me about this though, firstly with linear interpolation the second derivative term is zero. Is this an acceptable simplification?

Secondly, when calculating mass fluxes along the internal triangle edges you obviously have to take the integral of density and relative velocity (fluid velocity minus the velocity of that edge), but when calculating momentum fluxes I am not sure whether I ought to be taking relative velocity , absolute velocity, or a mix of both.

Third, I'm not convinced this would be fast enough even.

Ideally, I would like to be able to completely ignore the motion of the centre of the droplet, as it's only its free edge I'm interested in. Green's functions seem (?) to get use this, but I haven't found any particularly clear explanations of their use in a case like this. I guess I would then just do a low order IFFT to calculate the free surface.

Any help would be much appreciated.

Thanks,

Tom Holden