Modeling free surface flows in a CFD context typically requires an incompressible approach along with a formulation to account for the air–water interface. Commonly, pressure-correction algorithms combined with the Volume of Fluid (VOF) method are used to describe these kinds of flows. Pressure-correction algorithms are segregated solvers, which means equations are solved in sequence until convergence is accomplished. On the contrary, the artificial compressibility (AC) method solves a single coupled system of equations. Solving at each timestep a single system of equations obviates the need for segregated algorithms, since all equations converge simultaneously. The goal of the present work is to combine the AC method with VOF formulation and prove its ability to account for unsteady flows of immiscible fluids. The presented system of equations has a hyperbolic nature in pseudo-time, thus the arsenal of the hyperbolic discretization process can be exploited. To this end, a thorough investigation of unsteady flows is presented to demonstrate the ability of the method to accurately describe unsteady flows. Problems of wave propagation on constant and variable bathymetry are considered, as well as a fluid structure interaction problem, where viscous effects have a significant impact on the motion of the structure. In all cases the results obtained are compared with theoretical or experimental data. The straightforward implementation of the method, as well as its accurate predictions, shows that AC method can be regarded as a suitable choice to account for free surface flows.

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Solvers based on Boundary Element Method (BEM) are fast and they have proven to provide accurate results in a wide range of applications. On the other hand, computational fluid dynamics (CFD) solvers are high-fidelity tools able to account for viscous effects. However, they are computationally demanding. In the present work, the limitations of BEM solvers are exploited considering the case study of a moonpool type floater in which the viscous effects near the sharp edges of the body (vortex shedding) are not negligible. The BEM results are compared with the results from an unsteady Reynolds averaged Navier-Stokes (URANS) CFD solver and experimental data, while viscous corrections of the BEM method are assessed.

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