Characteristics-based modelling of flow problems: Dissertation

The method of characteristics is in principle an exact way to proceed to the solution of hyperbolic partial differential equations. The numerical solutions, however, are obtained in the fixed computational grid where interpolations of values between the mesh points cause numerical errors. The Piecewise Linear Interpolation Method, PLIM, the utilization of which is based on the method of characteristics, has been developed to overcome these deficiencies. The work concentrates on the following topics: First, the PLIM method has been applied to study the validity of the numerical scheme through solving various difficult flow problems to achieve knowledge for the further development of the method. Second, the mathematical and physical validity and applicability of the two-phase flow equations based on the SFAV (Separation of the two-phase Flow According to Velocities) approach has been studied. Third, the SFAV approach has been further developed for particular cases such as stratified horizontal two-phase flow. In calculating the fluid dynamics of nuclear power plants, two-phase flow has to be considered. Numerical methods that are applied to solve two-phase flow problems are generally inaccurate. The importance of accurate numerical methods is often underestimated because of the difficulties in the physical description of two-phase flow problems. The numerical errors and the deficiencies of the physical model do not correlate; they are separate problems, although and inaccurate numerical solution by itself may lead to nonphysical results. The conventional approach that has been taken to derive one-dimensional two-phase flow equations leads to nonphysical equations and to a mathematically ill-posed initial boundary value problem. Mathematically well-posed and physically reasonable equations can be formed with the SFAV approach. The mathematical and physical justification of these equations has been verified. The applicability of the PLIM code and the various forms of these equations in two-phase flow problems have been studied, especially in the case of horizontal two-phase flow, in which new results have been obtained for the flooding phenomenon.