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.