An Implicit Second-Order Numerical Method for Three-Dimensional Two-Phase Flow Calculations

A new numerical method for three-dimensional two-phase flow computations is presented. The method has been implemented within the FLICA-4 computer code, which is devoted to three-dimensional thermal-hydraulic analysis of nuclear reactor cores. This numerical method is based on a finite volume technique, where convective fluxes at cell interfaces are calculated with an approximate Riemann solver. A strategy for constructing this linearized Riemann solver, which extends Roe's scheme, to solve two-phase flow equations is described. Extension to a second-order-accurate method is achieved using a piecewise linear approximation of the solution and a slope limiter method. For advancing in time, a fully implicit integrating step is used. Some improvements performed to obtain a linearized implicit solution method that provides fast-running steady-state calculations are also presented. This kind of numerical method, which is widely used for fluid dynamic calculations, is proved to be very efficient for the numerical solution to two-phase flow problems.