Reynolds-Averaged Navier-Stokes (RANS) models are still widely used to simulate turbulent flows, especially in industry. When it comes to multiphase turbulent flows, this type of model is known to overproduce turbulence close to an interface. To investigate this phenomenon, the open source software Basilisk that solves the Navier-Stokes equations is used. This software uses cartesian grids to obtain a very fast and precise Volume of Fluid method to track an interface. It can also simulate complex geometries thanks to an embedded boundary method. A monophase RANS k − ϵ model has been implemented in this solver. A high Reynolds model is considered based on the wall model used by Launder and Spalding. The velocity profile has been linearized as proposed by Tamaki and al. [4] for a RANS Spalart-Allmaras turbulence model to obtain the correct surface friction, even when embedded solids are present inside the computational domain. This model is tested and validated on classical geometries proposed by the Turbulence Modeling Resource website, namely a flat plate and a bump in a channel. Then, an air-water channel studied experimentally is used to test the model in multiphase configuration. The slowdown of the flow has been reproduced due to the overproduction of turbulence close to the interface. To solve this issue, a corrective term is added to the ϵ equation based on a formulation proposed by Frederix and al. to increase the turbulent dissipation at the interface. This new multiphase RANS k −ϵ model is used on the air-water channel and good agreements are obtained with experimental results. This study opens the possibility to simulate multiphase turbulent flows on more complex domains.