A method for simulating the flow of a fluid inside a vessel of a nuclear reactor using a computer suitably programmed, the nuclear reactor comprising the vessel and a core positioned inside said vessel, the vessel including a fluid inlet orifice and a fluid outlet orifice, the core including a lower plate (41 A), an upper plate and nuclear fuel assemblies extending in an axial direction between the lower (41 A) and upper (41 B) plates, the core having a volume (Vol C) delimited by first and second interfaces in the axial direction, the first and second interfaces respectively corresponding to the lower and upper plates (41 A, 41 B), the fluid being able to flow inside the core between the assemblies, the method comprising the following step: - computing (120, 130), for the core volume (Vol C), the pressure of the fluid and the component(s) of the speed of the fluid, from an initial value of the speed or pressure of the fluid in the first interface and an initial value of the speed or pressure of the fluid in the second interface and using the fluid mass, movement quantity balance and energy balance equations of the fluid, the method being characterized in that it further comprises the following steps: - determining at least one additional volume (Vol PI, Vol PS) inside the vessel, the additional volume (Vol PI, Vol PS) being outside the core volume (Vol C) and situated at one of the ends thereof in the axial direction, the additional volume (Vol PI, Vol PS) being delimited by two interfaces in the axial direction, one of the two interfaces of the additional volume (Vol PI, Vol PS) being the first interface or the second interface, - computing (110, 140), for the additional volume (Vol PI, Vol PS) and using the mass balance, movement quantity balance and energy balance equations of the fluid, the pressure of the fluid and the component(s) of the speed of the fluid, from an initial value of the speed or pressure in one of the interfaces of the additional volume (Vol PI, Vol PS) and an initial value of the speed or the pressure in the other of the interfaces of the additional volume (Vol PI, Vol PS), and the computation of the pressure of the fluid and of the component(s) of the speed of the fluid is first done for a first volume among the additional volume (Vol PI, Vol PS) and the core volume (Vol C), and in particular in the interface among the first and second interfaces that is shared by the additional volume (Vol PI, Vol PS) and the core volume (Vol C), then the pressure of the fluid and of the component(s) of the speed of the fluid is computed for the second volume among the additional volume (Vol PI, Vol PS) and the core volume (Vol C), the initial value of the speed or pressure at the interface shared by the additional volume (Vol PI, Vol PS) and the core volume (Vol C) and for that computation step associated with the second volume then being the value of the corresponding variable among the speed and the pressure previously computed at said interface for the first volume. - computing (120, 130), for the core volume (Vol C), the pressure of the fluid and the component(s) of the speed of the fluid, from an initial value of the speed or pressure of the fluid in the first interface and an initial value of the speed or pressure of the fluid in the second interface and using the fluid mass, movement quantity balance and energy balance equations of the fluid, - determining at least one additional volume (Vol PI, Vol PS) inside the vessel, the additional volume (Vol PI, Vol PS) being outside the core volume (Vol C) and situated at one of the ends thereof in the axial direction, the additional volume (Vol PI, Vol PS) being delimited by two interfaces in the axial direction, one of the two interfaces of the additional volume (Vol PI, Vol PS) being the first interface or the second interface, - computing (110, 140), for the additional volume (Vol PI, Vol PS) and using the mass balance, movement quantity balance and energy balance equations of the fluid, the pressure of the fluid and the component(s) of the speed of the fluid, from an initial value of the speed or pressure in one of the interfaces of the additional volume (Vol PI, Vol PS) and an initial value of the speed or the pressure in the other of the interfaces of the additional volume (Vol PI, Vol PS), and