• Finite-volume, fully conservative approach
• 2D, 2D axisymmetric, and 3D
• Implicit pressure-based solver
• Incompressible Navier-Stokes equations
• Newtonian and Non-Newtonian fluids
• Steady and unsteady advection
• High-order convection schemes (2nd and 3rd order)
• GMRES with multigrid acceleration and AMG
• 3rd order Runge-Kutta time advection

LEVEL SET

The level set approach consists in solving a hyperbolic equation to track the interface on a fixed Eulerian grid, using a smooth signed-distance function, referring to the shortest distance to the front. Negative values correspond to one of the fluids and positive values to the other. The exact location of the interface corresponds to the zero level.

Material properties like density, viscosity and thermal conductivity are updated in time using this distance function.

The advantage of this method is that it dispenses with interface reconstruction employed in VOF, it can handle merging and fragmentation, and it permits identification of the exact location of the interface, which helps treat interfacial physics (e.g. turbulence, mass exchange).

Our Level Set method works on both Cartesian and skewed curvilinear grids.

It is accurate in that it uses 3rd to 5th order WENO scheme for space update and 5th order Runge-Kutta for time marching. It uses various re-distancing schemes, including fast marching, conserving thus mass up to 0.1% mass loss.

VOF

In the VOF context, TransAT solves for the evolution of the liquid volume-fraction, identifying flow regions containing pure liquid from pure gas flow regions. The VOF method does not amount solely to the solution of this evolution equation, it requires accurate algorithms for advecting the volume fraction function so as to preserve conservation of mass. Since this cannot be achieved by means of conventional finite-difference schemes because of numerical diffusion, the VOF field is first advected, after which the interface location is reconstructed.

The 3D VOF model of TransAT features two variants of unsplit advection, and  the multidimensional flux calculation using cell-face velocities assigned to cell-vertices (Piecewise-Constant Flux Surface Calculation, or PCFSC). The evolution of the interface and advection of the phase-indicator function is accomplished by reconstructing the interface within each computational cell and computing the volume flux that occurs from each cell to its immediate neighbours under the prevailing flow. Use is made of  the CVTNA high-order scheme of Liovic is used for interface reconstruction.

LES

In TransAT we have borrowed the LES strategy from single phase flows and coupled it with both VOF and Level Sets for small-to-mild Re fluid-fluid flows. The combination (referred to as LEIS) could lead to the simulation of the large-scale physics of interfacial flows down to the grid-resolved level.

 The idea consists of grid-filtering each phase separately; the resulting sub-grid scale (SGS) stresses are modelled as if they were isolated. Special treatment is necessary at the interface though, taking advantage of the fact that the lighter phase perceives the interfaces like deformable walls. The combination of the two brings a notable difference, that is: besides delivering time-dependent interfacial kinematics (and provided the method could achieve sufficient resolution for the boundary layers at the interfaces), the need to model the interfacial exchange terms in the two-fluid phase conservation equations is eliminated. For the time being this is limited to interfacial flows.

A rigorous near-interface treatment is included, taking into account the interfacial shear on both sides of the interface.