One of the key components of the nuclear reactor is the reactor pressure vessel (RPV), and its integrity is critical for the safety of the nuclear reactor. Lifetime extension of RPV project deals with the different issues which pose threat to its integrity. One such important issue is the occurrence of pressurised thermal shock (PTS). The most critical PTS scenario occurs during the events of loss of coolant accidents, when the emergency core cooling water is injected to cool down the reactor’s core. This cold water mixes with the hot water while descending in the downcomer of the RPV and result in sudden fluctuation in temperature of the vessel wall, giving rise to thermal stresses in it. Thermal-hydraulic codes, which are generally used for the nuclear reactor safety (NRS) applications, are unable to predict this complex 3-dimensional flow mixing phenomenon. Therefore, computational fluid dynamics (CFD) method are considered useful for the comprehensive study of PTS. However, the validation with the experimental data is required to gain trust in predictive capabilities of CFD methods for PTS studies. A high-fidelity direct numerical simulation (DNS) can provide the data for validation. Moreover, it can give more insight about the flow phenomenon and can form a reference database for the turbulence modelling CFD methodologies. The main aim of this thesis project is to perform an extensive preliminary study for the high-fidelity DNS of the single-phase PTS scenario. The objectives are, firstly to design a well defined and well studied numerical case for this DNS, which will be focused towards the buoyancy driven flow mixing in the downcomer of the RPV, and secondly to validate the DNS of a buoyancy driven flow mixing test case. With the help of several simulations, calibration study was performed to find an optimum physical domain and boundary conditions. In addition, a length scales study was performed which will help in mesh estimation for the DNS. Furthermore, a DNS of Rayleigh Bénard convection is performed and the results are compared with the results of a past DNS. This, in total, will contribute to the PTS studies in the direction which has not been dealt in the past and will form an essential basis for the future DNS of the PTS scenario.