| Numerical simulation method is one of the important research methods of wave-structure interaction in the field of ocean engineering.Numerical simulation methods can be divided into potential flow method and viscous flow method.In the potential flow theory,through a series of potential flow assumptions,the Laplace equation is used as the control equation.The greatest advantage of the potential flow method is the low computational cost which improves the computational efficiency.What’s more,there are more and more accurate numerical methods for the potential flow,since the form of the Laplace equation is not very complex.Therefore,the potential flow method is widely used for numerical solutions of large marine structures.However,the potential flow method is based on the potential flow hypothesis,and the viscous effect can not be ignored in some practical engineering applications,such as when the resonance effect appears or when the viscous resistance of the structure is very important.Therefore,it is necessary to use the viscous flow method as an analysis means to calculate the accurate flow field near the marine structures,so as to accurately predict and evaluate the marine structures.The projection method is one of the typical time discretization methods for solving Navier-Stokes(NS for short)equations in viscous field.The projection method decouples the velocity and pressure to for further spatial discretization of the Navier-Stokes equations.The spatial discretization of Navier-Stokes equation often includes the solution of convection equation,diffusion equation and Poisson equation.Poisson equation is of vital important for the accuracy and efficiency of Navier-Stokes equation.The accuracy the Poisson equation is related to the pressure field,and the computation cost of the Poisson equation is large,especially for the solution of the variable-coefficient Poisson equation in the two-phase flow.In addition,another challenge is that the computation cost of simulation with large Reynolds number affects the efficiency of numerical calculation.The Harmonic Polynomial Cell which is referred to as the HPC method was first proposed by Shao and Faltinsen based on the potential flow theory for solving the Laplace equation.In the two-dimensional HPC method,the HPC method is verified as the fourth-order accuracy based on the nine stencil points where a series of harmonic polynomials are used to construct the approximate solution.Due to high-order computational accuracy and efficiency of the HPC method,it has been quickly extended to three-dimensional and become very popular in potential field.Bardazzi et al.extended the HPC method for solving the two-dimensional Poisson equation with constant coefficients,which is called GHPC(Generalized Harmonic Polynomial Cell,referred as GHPC).On the basis of the original HPC method,the GHPC method introduces biquadratic interpolation and combines more high-order polynomials,and finally achieves the fourth-order high precision with body-fitted grids.Thus,this thesis proposes an immersion boundary treatment method for the GHPC method,and successfully develops a Poisson equation solver based on the GHPC method on Cartesian grid,so that it can be directly applied to the projection method to solve Navier-Stokes equation,which improves the accuracy of solving Poisson equation in Navier-Stokes equation.What’s more,In order to improve the computational efficiency of the numerical model for the large Reynolds number problem,the turbulence model and wall function are combined in the solver,where the computational complexity of the numerical model is effectively reduced on the basis of ensuring the calculation accuracy.This provides a new way to solve the problem of large Reynolds number calculation in ocean engineering.The main research works of this dissertation are as follows:First,a fourth-order constant-coefficient Poisson equation solver is built on Cartesian grid.The GHPC method is induced based on body-fitted grid and implemented in uniform grid.In this thesis,a strategy for the GHPC method on immersed grids is proposed to extend GHPC method from body-fitted grid to fixed Cartesian grid,and the GHPC method is further extended and applied on non-uniform grid.Second,the GHPC method is implemented into solving the Poisson equation in projection method,and a single-phase flow Navier-Stokes equation solver is developed combining with the Finite Difference Method(referred as FDM).In this thesis,the accuracy of the solver are verified by calculating a series of problems,such as Taylor Green analytical function,the cavity flow,flow around a cylinder and flow around a square cylinder.Third,based on the single-phase flow solver,the k-ω turbulence model is applied to construct a numerical model for the case of large Reynolds number.Meanwhile,wall functions of k-ω turbulence model is successfully combined with the immersion boundary method by the proposed strategy.The small-scale of viscous layer calculating near the wall is avoid,thus number of grids is reduced and the computational efficiency is improved at the same time.Finally,the model is verified by the typical channel flow problem.What’s more,by introducing the pressure correction method,the GHPC method is extended to solve the variable-coefficient Poisson equation,which is involved in projection method for two-phase flow Navier-Stokes.Meanwhile,we apply volume of fluid method for capture of the free surface,and develops a two-phase flow Navier-Stokes equation model based on the GHPC method in solving the Poisson equation.In this thesis,problems of liquid tank sloshing,wave propagation,wave propagating over breakwater is fully verified.Finally,the current solution model is used to investigate the hydrodynamic performance of a perforated plate in oscillating flow,orbital flow and incident waves,and is applied to the study free surface effect on the perforated plate. |
