A novel Godunov-type scheme for free-surface flows with artificial compressibility

Variable density incompressible flows are governed by parabolic equations. The artificial compressibility method makes these equations hyperbolic-type, which means that they can be solved using techniques developed for compressible flows, such as Godunov-type schemes. While the is well-established, its application to variable has been largely neglected in literature. This paper harnesses recent advances wider field applying a more robust Riemann solver and easily parallelisable time discretisation than previously. We also develop new calculating pressure gradient part of second-order reconstruction step. Based on rearrangement momentum equation an exploitation other gradients source terms, calculation automatically captures discontinuity at free surface. Benchmark tests demonstrate improvements gained this calculation.