Verification of a homogeneous micture model for the free surface problem: Master's thesis

In this thesis, the applicability of the homogeneous mixture model of FINFLO for the free surface problem is studied. The free surface problem is fundamental in marine hydrodynamics, and a special case in two-phase flows. The work explores the basis of this type of modelling from mathematical and numerical viewpoints, and verifies the mixture model for the problem. The mathematical background of the problem is presented, together with the nature of it from the perspective of marine hydrodynamics. The bulk flow equations are usually averaged conditionally such that the governing equations of the multiphase model are formally the same as in the case of single-phase flow. It can be shown that one additional equation suffices for the description of the segregated phases. Here, the convection equation of the void fraction is utilized. The void fraction equation is derived in conservative form based on the incompressibility constraint of the individual phases. The convection of the void fraction corresponds to the so-called Riemann problem. This is studied thoroughly by developing a two-dimensional solver for the comparison of some well-known schemes for the spatial discretization of the convective quantity. This solver is applied to the convection of a discontinuous distribution of the void fraction. In addition, the so-called SUPERBEE limiter is implemented to the FINFLO code for the extrapolation of the convective void fraction. The numerical solution of the Navier-Stokes equations for simulations of two-phase flows is covered comprehensively. The code YAFFA, developed at the Aalto University, has a modern VOF model implemented, and for this reason, it is here used as a reference code. The solution algorithms, the computation of the convective quantities, the pressure correction stages as well as the treatment of the segregated phases in both of the codes are discussed in detail. The two-phase flow over a submerged ground elevation is computed using the codes FINFLO and YAFFA, and the forming free surface wave is compared to the corresponding results found from the literature. The aim of this thesis is to get acquainted with the nature of the problem in conjunction with the specific methodology used to solve such flows. This is done in order to understand the requirements and possible modifications needed for the model when we wish to accurately predict ship flow phenomena that are not solvable using the traditional free surface tracking strategies. This way, the verification of the mixture model of FINFLO is achieved.