A viscous numerical wave tank based on immersed-boundary generalized harmonic polynomial cell (IB-GHPC) method: Accuracy, validation and application

A novel two-dimensional numerical wave tank based on the two-phase Navier–Stokes equations (NSEs) is presented. The popular projection method is applied to decouple the pressure and velocity fields, while the solutions are uniquely enhanced by a newly-developed immersed-boundary generalized harmonic polynomial cell (IB-GHPC) method for the pressure Poisson equation, which lies at the heart of the projection method. The GHPC method, originally proposed for the constant-coefficient Poisson equation, has been employed in solving the single-phase NSEs with success, though it cannot be directly applied for two-phase flows. In this paper, we show that the GHPC method can still be used in solving two-phase flow problems by introducing a pressure-correction method. By considering wave generation and propagation, the accuracy and convergence rate of the present numerical model is demonstrated. The solver is further validated against model tests for wave propagation over a submerged breakwater, and a perforated plate in oscillatory flows and incident waves. Excellent agreement with benchmark results confirms the accuracy and the validity of the new numerical wave tank towards more general wave–structure-interaction problems. The free-surface effect on the wave loads of a perforated plate is further investigated through applications of the present numerical model.