## Introduction

**IHFOAM 1.0** solves the three-dimensional Reynolds Averaged Navier-Stokes (RANS) equations for two incompressible phases using a finite volume discretization and the volume of fluid (VOF) method. In VOF, each phase is described by a fraction α occupied by the volume of fluid in the cell. This technique allows very complex free surface configurations to be represented easily and involves no mesh motion. It also supports several turbulence models (e.g. κ−ε , κ−ω SST, LES).

**IHFOAM** solver is prepared for static meshes. **IHDyMFOAM** is an enhanced version of it, which handles remeshing after each time step (“DyM” stands for dynamic mesh). Hence it can simulate floating body movements or support dynamic mesh refinement along the free surface, while solving the same equations and following the same procedures.

## Governing equations

The aforementioned RANS equations include continuity and mass conservation equations, which are presented below. The assumption of incompressible fluids has been used.

Along with these governing mathematical expressions, which describe the motion of fluid flow, an additional one must also be taken into account to describe the movement of the phases. The starting point is an advection equation. However, as the interface should be maintained sharp, an artificial compression term is added.

The equation remains conservative with such a term. The solution must be bounded between 0 and 1. This restriction is achieved using a solver called MULES (Multidimensional Universal Limiter for Explicit Solution).

## Solving procedure

The solving algorithm is called PIMPLE, which is a mixture between PISO (Pressure Implicit with Splitting of Operators) and SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithms. PIMPLE main structure is inherited from the original PISO, but it allows equation under-relaxation, as in SIMPLE, to ensure the convergence of all the equations at each time step.

A detailed flow chart of the main loop can is presented below. The alpha subcycle and the PIMPLE loop are further developed outside it.