Numerical Simulation of Solitary Wave Breaking With Adaptive Mesh Refinement

The numerical simulation of wave breaking problem is still a tough challenge, partly due to the large grid number and CPU time requirement for capturing the multi-scale structures embedded in it. In this paper, a two-dimensional two-phase flow model with Adaptive Mesh Refinement (AMR) is proposed for simulating solitary wave breaking problems. Fractional step method is employed for the velocity-pressure decoupling. The free surface flow is captured with the Volume-of-Fluid (VOF) method combined with Piecewise Linear Interface Calculation (PLIC) for the reconstruction of the interface. Immersed boundary (IB) method is utilized to account for the existence of solid bodies. A geometric multigrid method is adopted for the solution of Pressure Poisson Equation (PPE). Benchmark case of advection test is considered first to test the VOF method. Then the solitary wave propagation problem is utilized to validate the model on AMR grid as well as analyze the efficiency of AMR. Furthermore, the solitary wave past a submerged stationary stage problem is simulated to validate the combined IB-VOF-AMR model. All the numerical results are compared with analytic solutions, experimental data or other published numerical results, and good agreements are obtained. Finally, the influence of stage height on the occurrence of wave breaking is analyzed. The locations of wave breaking are summarized for different stage heights.