Study for the computational resolution of conservation equations of mass, momentum and energy. Application to laminar flows in cavities and introduction to turbulence modelling

The use of numerical methods as a tool to solve differential equations allows for solving problems whose analytical solution is unfeasible given the current calculation techniques. Their application in the field of fluid dynamics is based on dividing a domain into a finite number of control volumes; the greater this number is, the closer the numerical solution approximates what would be the analytical solution of the problem. The Navier-Stokes equations, which express the conservation of mass, momentum, and energy of the corresponding fraction of fluid at a given moment, are applied to each control volume. This thesis provides an introduction to the numerical resolution of the Navier-Stokes equations, using a simplified formulation through certain hypothesis, with the aim of providing the author with the foundational knowledge to apply this methodology to problems in both academic and industrial fields. The results of the work demonstrate that the physical conditions of a problem, which can be quantified through the Reynolds number, or Rayleigh number in cases with natural convection, significantly affect the computational requirements to obtain its numerical solution. This numerical solution is infinitesimally close to the analytical one if grid and time step convergences are met, meaning that the number of control volumes is sufficiently high and the simulated time between one moment and the next is sufficiently small. The Reynolds number allows for establishing whether a problem corresponds to laminar (the flow is orderly and, to some extent, predictable; low value) or turbulent (the flow behaves chaotically; high value) regime. The results show a conspicuous trend towards requiring more control volumes and smaller time steps as this physical parameter increases. For this reason, the computational power can become excessive if a turbulent flow problem needs to be resolved. The most effective solution in these cases is to apply turbulence models, such as LES or RANS, instead of solving all scales of the flow, ...