Study for the computational resolution of conservation equations of mass, momentum and energy. Numerical analysis and turbulence models

Abstract

his undergraduate thesis presents a study on the numerical solution of the Navier-Stokes equations under various assumptions. To achieve this, several codes have been developed in C++ language to evaluate and verify the cases proposed by the Heat Transfer Technological Center (CTTC). The thesis is divided into different chapters. Firstly, there is an introduction to numerical methods, where spatial and temporal discretizations are explained, along with algorithms for solving systems of equations. Then, the main body of the work consists of four chapters. The first chapter addresses the heat conduction phenomenon and solves a transient two-dimensional conduction case. The second chapter deals with the general convection-diffusion equation and applies it to four problems to validate the code. The third chapter implements the Fractional Step Method (FSM) and solves the Lid-Driven Cavity, Differential Heated Cavity, and Square Cylinder cases. The fourth chapter solves the Burgers’ equation in the Fourier space. All four chapters include theoretical development, the algorithm’s structure for solving the case, and one or several verification cases, along with their respective reference results. Finally, there is a last chapter about the Turbulent Flow problem, where the extension to three dimensions of the numerical algorithm is explained.