Volume Fractions in PySPH

Volume Fractions is a method to simulate multiple materials in SPH. Instead of having particles made up of a single material, the particles are split into fractions of different materials. This works especially well to handle the dissolution of small amounts of solute in solvent, because if they had to be represented by pure particles, small ratios would require too many particles.

Different methods

Krištof, P., Beneš, B., Křivánek, J., & Št'ava, O. (2009) Hydraulic erosion using smoothed particle hydrodynamics.

In this paper, erosion from rivers is simulated in 3D using SPH. Erosion in rivers occurs when the shear force of water picks up particulates such as mud or silt from the bottom. Material is transferred between particles using the donor-acceptor scheme. The solid material is suspended in the water, and slowly settles down to the bottom, depositing when the liquid velocity is low.

The solid bottom of the river is simulated by placing sph particles on the surface of a mesh and running liquid over it. The authors use an algorithm to shrink and expand the mesh based on how much material the border particles are losing or gaining.

Ren, B., Li, C., Yan, X., Lin, M. C., Bonet, J., & Hu, S.-M. (2014) Multiple-fluid SPH simulation using a mixture model.

In this paper, the researchers demonstrate a versatile framework for simulating multiphase flow. They use the standard Volume Fraction technique, in which mixture particles consist of fractions of different phases/materials.

Their technique can handle diffusion, miscible and immiscible flows, interactions between liquid and gas, and chemical reactions.

The Mixture Particle

It has a density, velocity, and pressure. It also can contain multiple phases with their own densities, velocities, and pressures.

They use a term called drift velocity, which are the different directions the volume fractions of a particle are going. There is a nice diagram of how the sum of the phase velocities is the velocity of the mixture particle, and how the mixture velocity is then subtracted from the phase velocities to obtain the drift velocities.

What isn't clear to me is how the equations work. It takes a while just to write out what each symbol means, let alone understand the relationships between them. I will have to look at this more.