Study for the numerical resolution of conservation equations of mass, momentum and energy to be applied to the aerodynamics of airfoil-shaped bodies

Abstract

A set of benchmark problems concerning laminar and incompressible flows are solved by means of self-developed software written in C++ language and based in the Finite Volume Method. This problems include the Smith-Hutton problem, the Lid Driven Cavity and the Differentially Heated Cavity, as well as an approach to turbulence phenomenon with Burgers' equation (in this case spectral methods are to be used). Developed codes are verified through comparisons with benchmark solutions and through the analysis of the order of accuracy of the obtained results. A specific case of study on external flow analysis is done, including the resolution of a confined flow past a square cylinder aiming to solve flows over more complex geometries such as airfoil-shaped bodies. Finally, recommendations on how to extend this study to turbulent and compressible flows are presented