The most accurate way to know the movement of the neutrons through matter is achieved by solving the Neutron Transport Equation. Three different approaches to solve this equation have been investigated in this thesis: Discrete Ordinates Neutron Transport Equation, Neutron Diffusion Equation and Simplified Spherical Harmonics Equations. In order to solve the equations, different schemes of the Finite Differences Method were studied. The solution of these equations describes the population of

more »

... rons and the occurred reactions inside a nuclear system. These variables are related with the flux and power, fundamental parameters for the Nuclear Safety Analysis. The thesis introduces the definition of the mentioned equations. In particular, they are detailed for the steady state case. The Modal Method is proposed as a solution to the eigenvalue problems determined by the equations. First, several algorithms for the solution of the steady state of the Neutron Transport Equation with the Discrete Ordinates Method for the angular discretization and Finite Difference Method for spatial discretization are developed. A formulation able to solve eigenvalue problems for any number of energy groups, with scattering and anisotropy has been developed. Several quadratures used by this method for the angular discretization have been studied and implemented for any order of approach of the discrete ordinates. Furthermore, an adapted formulation has been developed as a solution of the source problem for the Neutron Transport Equation. v Next, an algorithm is carried out that allows to solve the Neutron Diffusion Equation with two variants of the Finite Difference Method, one with cell centered scheme and another edge centered. The Modal method is also used for calculating any number of eigenvalues for several energy groups and upscattering. Both Finite Difference schemes mentioned before are also implemented to solve the Simplified Spherical Harmonics Equations. Moreover, an analysis of different approaches of the boundary conditions is performed. Finally, calculations of the multiplication factor, subcritical modes, neutron flux and the power for different nuclear reactors were carried out. These variables result essential in Nuclear Safety Analysis. In addition, several sensitivity studies of parameters like mesh size, quadrature order or quadrature type were performed. vi Por otro lado, también quiero dar las gracias a todos los que integran el Departamento de Ingeniería Química y Nuclear de la Universidad Politécnica de Valencia. En particular agradecer a Gumersindo Verdú, sus continuos debates en xiii investigación; a Belén Juste por su gran ayuda, asesoramiento y colaboración en muchas investigaciones; a José Rodenas por ofrecerme siempre una nueva formación y a Antoni Vidal por compartir sus conocimientos. De la misma forma, quisiera extender mis agradecimientos a mis compañeros de departamento, en especial a Carles, Consuelo y Antonella, pero sin olvidarme de Amanda, Patricio, Aina, Nico, María, Javier, Sete y Marina. Agradezco a mis amigos de Valencia y Denia todos sus detalles y por estar siempre presentes en mi día a día. Por último, pero no menos importante, agradezco el apoyo de mi familia, mis hermanos y mi padre; y a los que me hacen sentir como tal, Jesús y Nati. Muy especialmente quiero dar las gracias a María, por estar siempre a mi lado e invitar a superarme. Finalmente, sería injusto no acordarme de mi madre a quien debo todo lo que soy. xiv