Correcting the Semi-Implicit Numerical Scheme Incorporated in the KORSAR Code Two-Liquid Model

Abstract

Two algorithms used to correct the semi-implicit numerical scheme for time integration of the conservation equations incorporated into the KORSAR/GP computer code two-liquid model are presented. The KORSAR/GP code has been developed jointly by specialists of the Federal State Unitary Enterprise Aleksandrov Research Institute of Technology and Gidropress Experimental Design Office; in 2009, the code was certified at the Federal Service for Environmental, Technological, and Nuclear Supervision (Rostekhnadzor) as applied to numerical safety assessment of VVER-based reactor plants. In the semi-implicit scheme, the convective terms appearing in the phase momentum conservation equations are written in an explicit form. The mass and energy flows of the phases are represented implicitly with respect to phase velocities, and the transferred donor quantities are calculated based on the parameters taken from the previous time layer. Owing to linearization of unsteady and source terms, the linear system of finite difference equations is solved in a noniteration manner. The first of the presented algorithms compensates for numerical imbalances of phase masses and energies resulting from linearization of unsteady terms appearing in the discrete equations and ensures conservativeness of the scheme. The second algorithm introduces correction for the nonphysical redistribution of coolant mass and energy over the computational cells if a change occurs in the phase motion direction within a time step when the scheme of approximating the convective terms becomes “antidonor” with respect to flow. The numerical imbalances and refinements taking into account the correction of donor quantities are computed at each time step according to the proposed correlations and are used for making compensation at the next time step as supplementary sources in the conservation equations. Results from testing the correction algorithms in the KORSAR/GP code are presented. The effectiveness of the imbalance compensation algorithm is confirmed by solving a problem involving the natural circulation loop heating process. The adequacy of the “antidonor” scheme correction algorithm is demonstrated on problems involving steplike initial distribution of the scalar parameters of a stagnant single-phase gaseous or water coolant in a horizontal tube when the flowrate at the tube inlet has different signs at different time steps.