Author(s): J. W. Lee; M. D. Teubner; J. B. Nixon; P. M. Gill
Linked Author(s): Joseph Hun-Wei Lee
Keywords: Rtificial compressibility method; Hydrodynamic pressure; Free surface flows; K-ε turbulence model
Abstract: A three-dimensional numerical method for solving free surface flows with a standard k-ε turbulent closure is presented. In order to couple pressure with velocity directly, the pressure is divided into hydrostatic and hydrodynamic parts and the artificial compressibility method is employed for the hydrodynamic pressure. By introducing a time derivative of the hydrodynamic pressure into the continuity equation, the incompressible Navier–Stokes equations are changed from elliptic-parabolic to hyperbolic-parabolic equations. This helps to maintain a numerical scheme which is highly accurate for the hyperbolic terms. In this paper, a third-order monotone upstream-centred scheme for conservation laws (MUSCL) method is used. A system of discrete equations is solved implicitly using the lower-upper (LU) symmetric Gauss–Seidel method. This newly developed numerical method is validated against experimental data with very good agreement.