Bernard, Manuel; Dellacherie, Stéphane; Faccanoni, Gloria; Grec, Bérénice; Penel, Yohan Study of a low Mach nuclear core model for two-phase flows with phase transition I: Stiffened gas law. (English) Zbl 1304.35529 ESAIM, Math. Model. Numer. Anal. 48, No. 6, 1639-1679 (2014). Summary: In this paper, we are interested in modelling the flow of the coolant (water) in a nuclear reactor core. To this end, we use a monodimensional low Mach number model supplemented with the stiffened gas law. We take into account potential phase transitions by a single equation of state which describes both pure and mixture phases. In some particular cases, we give analytical steady and/or unsteady solutions which provide qualitative information about the flow. In the second part of the paper, we introduce two variants of a numerical scheme based on the method of characteristics to simulate this model. We study and verify numerically the properties of these schemes. We finally present numerical simulations of a loss of flow accident (LOFA) induced by a coolant pump trip event. Cited in 11 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 35Q79 PDEs in connection with classical thermodynamics and heat transfer 65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs 76T10 Liquid-gas two-phase flows, bubbly flows Keywords:low Mach number flows; modelling of phase transition; analytical solutions; method of characteristics; positivity-preserving schemes PDFBibTeX XMLCite \textit{M. Bernard} et al., ESAIM, Math. Model. Numer. Anal. 48, No. 6, 1639--1679 (2014; Zbl 1304.35529) Full Text: DOI