[en] Full text: The numerical aspects involved in the prediction of fluid-dynamic instabilities are shortly reviewed, mainly addressing single-phase natural circulation flows. In particular, some open literature, produced since the pioneering work of Welander (1967) and related to single-phase thermosyphon loops is firstly considered; then the analysis turns to summarize some early calculations and examples of code verification results dealing with the prediction of single-phase natural circulation, having in mind the goal of getting insights for the use of system thermal-hydraulics codes. In this perspective, the work previously performed in relation to Welander's problem and other relevant single-phase thermosyphon loop cases is reviewed, with main emphasis on the adopted methodology, based on numerical discretization of governing equations. One of the uses of this methodology is to check the effect of the nodalization on the appearance of oscillations once a theoretical (i.e., exact) stability map for the prototype problem is defined. In this way, it is possible to define the limits of applicability of a coarse nodalization to be used in transient calculations. These results serve to illustrate how time domain codes may be used to analyze these problems and also the effect of considering different constitutive laws in the computed linear stability map. Reference to the application of this methodology to boiling channel stability analysis is also made to demonstrate its generality. It must be emphasized that the results show both the qualitative and quantitative details of the changes that stability maps undergo as a consequence of numerical discretization of governing equations. Finally, the recent attempt to make easier the application of the methodology by the use of automatic FORTRAN code differentiation tools is reported, showing quantitative results concerning automatic calculation of the sensitivity of simulations results to physical and numerical parameters. (author)