Computational simulation of compressible flowsA family of very efficient and highly accurate numerical methods based on Finite Differences

Resumen

Given the large scale of industrial processes, usually a small tweak in a small part of the process can lead to a huge overall savings. This is one of the reasons why there is a growing interest in Computational Fluid Dynamics. The numerical simulation has become a fundamental tool to understand all the variables that intervene in a certain aerodynamic phenomenon and has proven to be of great help when solving problems of interest in Engineering. In this Thesis, high-order numerical methods applied to compressible flows will be developed. Firstly, the formulation of a hybrid method of centered Finite Differences and Weighted Essentially Non-Oscillatory (WENO) schemes combined with an a posteriori methodology will be described. The present formulation is able to obtain accurate results using less computational resources than the schemes present in the bibliography. The second part of this Thesis focuses on designing a method that allows to impose boundary conditions with arbitrary high order. This methodology is able to maintain the accuracy of a high-order numerical method in problems with curved boundaries using Cartesian meshes. A constrained least-squares polynomial reconstruction is used and it allows to impose a general boundary condition of the Robin type. This technique is totally independent of the spatial scheme that is used. The last part deals with the creation of a method with adaptive dissipation of application to the family of WENO schemes to improve the results when these methods are applied to problems with turbulent flows. This new formulation allows to modify locally the numerical dissipation introduced in each moment of time. Thus, this methodology acts as an implicit turbulence model that allows for the resolution of problems with turbulent flows.