This thesis presents an introduction to computational fluid dynamics (CFD), focusing on the mathematical modeling and numerical solution of fluid flow problems. The study is divided into three parts: the mathematical model of a fluid, the discretization of differential equations, and computational solutions of fluid flow properties. The first part defines the mathematical framework for fluid dynamics, including the definition of a fluid, its properties, and the Navier-Stokes equations, which describe the motion of fluids. The Navier-Stokes equations are derived from the principles of conservation of mass and momentum. The study also introduces the concept of incompressible and homogeneous fluids, and discusses the stress tensor, which represents the internal forces acting on a fluid. The second part focuses on the discretization of differential equations. It discusses two spatial discretization methods: finite difference and control volume methods. The temporal discretization is also covered, including explicit and implicit schemes. The study provides an example of discretization using these methods, focusing on the convective and diffusive terms in the Navier-Stokes equations. The third part presents two examples of fluid dynamics problems solved computationally. The first example involves the convective-diffusive transport of a scalar property in a fluid. The second example is a driven-cavity problem, where a fluid initially at rest is subjected to a moving boundary condition. The study uses the fractional step method and control volume discretization to solve these problems and compares the results with reference values. The study emphasizes the importance of a solid mathematical framework for computational simulations of fluid dynamics. It also highlights the role of the Reynolds number in determining the similarity of fluid flows and the significance of the Helmholtz-Hodge decomposition in understanding the behavior of pressure in incompressible fluids. The research is conducted in collaboration with the Centre Tecnològic de Transferència de Calor (UPC) and is supervised by Dr. Angel Jorba.This thesis presents an introduction to computational fluid dynamics (CFD), focusing on the mathematical modeling and numerical solution of fluid flow problems. The study is divided into three parts: the mathematical model of a fluid, the discretization of differential equations, and computational solutions of fluid flow properties. The first part defines the mathematical framework for fluid dynamics, including the definition of a fluid, its properties, and the Navier-Stokes equations, which describe the motion of fluids. The Navier-Stokes equations are derived from the principles of conservation of mass and momentum. The study also introduces the concept of incompressible and homogeneous fluids, and discusses the stress tensor, which represents the internal forces acting on a fluid. The second part focuses on the discretization of differential equations. It discusses two spatial discretization methods: finite difference and control volume methods. The temporal discretization is also covered, including explicit and implicit schemes. The study provides an example of discretization using these methods, focusing on the convective and diffusive terms in the Navier-Stokes equations. The third part presents two examples of fluid dynamics problems solved computationally. The first example involves the convective-diffusive transport of a scalar property in a fluid. The second example is a driven-cavity problem, where a fluid initially at rest is subjected to a moving boundary condition. The study uses the fractional step method and control volume discretization to solve these problems and compares the results with reference values. The study emphasizes the importance of a solid mathematical framework for computational simulations of fluid dynamics. It also highlights the role of the Reynolds number in determining the similarity of fluid flows and the significance of the Helmholtz-Hodge decomposition in understanding the behavior of pressure in incompressible fluids. The research is conducted in collaboration with the Centre Tecnològic de Transferència de Calor (UPC) and is supervised by Dr. Angel Jorba.