Three fluid mixing

The Gales formulation can be applied with no modification to any arbitrary number of fluids with different densities. In this example we check the behavior with three different fluids with different densities and same viscosity (mu = 0.1 Pa s). The computational domain is a 1 x 1 m cavity, with free-slip walls and gravity force g = 10 m/s².

In the initial configuration, fluid A is in a stable position, but fluids B and C will move to find the stable horizontal
stratification. Figures below show the fluids positions at different time steps. During the first time steps fluid C moves from right to left by the bottom part of the domain while fluid B moves from left to right by the upper part. The movement is so sudden that at time t = 15 s some fluid C get trapped inside fluid A on the right hand side. Due to their higher density, it moves downwards later. With respect to the reference solution, this last motion is not reproduced by our computations.

The grid is subdivided into 200 x 200 square elements (mesh.geo), the time step is 1e-2 s.

The diagonal tau of 2014 is set in the setup.txt file.

Custom properties of the three fluids are assigned in props.txt file.

Initial and boundary conditions are set in fluid_ic_bc.hpp file.

The comparison of Gales results and the reference solution are shown below.

Reference

Sergio Idelsohn, Monica Mier-Torrecilla, Eugenio Oñate “Multi-fluid flows with the Particle Finite Element Method” (2009) CMAME