# Computational Fluid Dynamics Numerical Methods for Multiphase Simulations

Much of the development work we have done in this area expands upon the Volume-of-Fluid (VOF) method. The VOF method is a Computational Fluid Dynamics (CFD) technique for modeling immiscible multiphase fluid systems at the lengthscale of the immiscible phase interface (for example, a single deforming drop or breaking wave).

The idea behind the VOF method is simple: The location of each fluid phase is stored (computationally) as the volume fraction of that phase averaged over the volume of each cell in the computational mesh.

## Quantifying the accuracy of Volume of Fluid (VOF) methods

One advantage of the VOF method over alternative methods is that as volumetric data is used to store interface location, conservation of volume is guaranteed (assuming incompressible fluids). Basing the calculation on volumetric data has its disadvantages though: As geometric information about the interface geometry is not directly stored, VOF function advection and surface tension force calculation must be performed carefully to ensure that simulations are physically accurate. Improving the numerical techniques used for these processes and quantifying the accuracy of these techniques is the focus of the work in this area.

As phase volume fractions undergo step changes from one location to another in immiscible fluid systems, special techniques are required to advect (advance) the phase fractions (VOF functions). These techniques usually use a two step process:

• reconstruct the shape of the interface using stair-step, line or curve geometries in each computational cell, followed by
• calculating the flux of each fluid phase through each computational cell boundary based on this reconstructed interface using either an operator split or multi-dimensional technique

Errors can be introduced in both of these steps.

Section under construction

## Viscoelastic immiscible fluid flows simulated using Volume of Fluid (VOF) methods

Above: Simulation of a PEO solution droplet (MW=5x10^5) forming and falling in air. The shading represents the trace of the polymer configuration tensor, which is a measure of the local average length of the polymers.
Above: Simulation of a PEO solution droplet (MW=10^6) forming and falling in air. The shading represents the trace of the polymer configuration tensor, which is a measure of the local average length of the polymers.

Section under construction