Numerical Simulations Of Water Wave And Its Influence

Incompressible flow field with free surface is simulated by the incorporation of an incompressible solver and a single phase level set approach on unstructured meshes. Water plays the role of incompressible flow field and water wave is the free surface. The Incompressible flow field governing equations are incompressible Euler equations which are solved by the application of Chorin`s artificial compressibility method. This method converts the continuity equation into time-marching form and permits the experience gained in the numerical solution of hyperbolic compressible flow problems to be exploited in the solution of incompressible flow problems. The cell-vertex finite volume scheme is used while the discretisation of convective fluxes is Roe`s scheme and the temporal discretisation is the implicit LU-SGS method. Because of the large density ratio of water and air, the water surface can be considered as a free surface without the force from the air. Then, it is reasonable to apply the single-phase level set method to simulate the water surface where the simulation of the air side is ignored and the solution variables are extrapolated from the water side into the air to supply proper artificial boundary conditions for both Euler and level set equations. The single-phase level set method is a surface capture method which defines a level set parameter throughout the whole compute region. This parameter is a signed distance from the free surface. For the nodes near the interface, the typical level set equation is calculated to transport the parameter. For other nodes away from the interface, a special reinitialization equation is used to guarantee the distance property of the parameter. For simplicity, the reinitialization step of typical level set method is replaced by a Laplacian equation which is calculated by finite element method. The simulation is demonstrated by using a submerged hydrofoil as a test case. Results agree well with both experimental data and another numerical data of surface fitting method. Finally, two contrast test cases with or without water wave are simulated in order to reveal the influence of water wave.