# Poisson solvers?

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#### abzug

I'm sure this seems pretty random, but since there are engineers around here someone might be familiar with simulation and be able to help me out.

I'm using smoothed particle hydrodynamics for a real-time simulation intended for computer graphics application (rather than accuracy), which runs at a good frame rate with as much as 20,000 particles on a quad core Intel (I spent some time getting things to parallelize nicely). My problem is stability in a tall column of fluid--I'm using a weakly compressible fluid (pressure computed from density by Tait's equation) and if restricted to a tall and thin vessel resulting into many layers of particles, under gravity, the liquid bounces a lot. If the gravity is high, the simulation blows up. One solution is applying a stability criterion to determine the maximum allowable timestep, but reducing the timestep artificially makes the simulation non-realtime, so this is not an acceptable solution for this application.

I've read that a fully incompressible SPH simulation can be done by using a pressure projection step, which needs solving a Poission equation. This is not something I'm familiar with and I'm wondering which solving algorithm to use, and how to specify boundary conditions (the fluid is free-surface).

#### d to the g

Paid Member
abzug said:
I'm sure this seems pretty random, but since there are engineers around here someone might be familiar with simulation and be able to help me out.

I'm using smoothed particle hydrodynamics for a real-time simulation intended for computer graphics application (rather than accuracy), which runs at a good frame rate with as much as 20,000 particles on a quad core Intel (I spent some time getting things to parallelize nicely). My problem is stability in a tall column of fluid--I'm using a weakly compressible fluid (pressure computed from density by Tait's equation) and if restricted to a tall and thin vessel resulting into many layers of particles, under gravity, the liquid bounces a lot. If the gravity is high, the simulation blows up. One solution is applying a stability criterion to determine the maximum allowable timestep, but reducing the timestep artificially makes the simulation non-realtime, so this is not an acceptable solution for this application.

I've read that a fully incompressible SPH simulation can be done by using a pressure projection step, which needs solving a Poission equation. This is not something I'm familiar with and I'm wondering which solving algorithm to use, and how to specify boundary conditions (the fluid is free-surface).

From the title of your post, I was pretty sure I was going to be able to help out as I work in the mechanical properties of nanostructures.

But I have absolutely no background in using Poisson for fluids. A nice treatment of Poisson as a function of shear can be found in Boresi, but since fluids have no resistance to shear I'm wouldn't no where to begin.

Good luck!

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