Implementation of an arbitrary-order Finite-Volume Least-Squares WENO for inviscid Euler equations

Rafael Castro Mota

Key information

Authors:

Rafael Castro Mota (Rafael Castro Mota)

Supervisors:

Duarte Manuel Salvador Freire Silva de Albuquerque (Duarte Manuel Salvador Freire Silva de Albuquerque)

Published in

11/08/2021

Abstract

In this thesis, an arbitrary order Least-Squares-WENO (LS-WENO) scheme will be applied for both the one-dimensional and two-dimensional finite volume formulation of the Euler equations. WENO schemes work by defyning several data sets (stencils) for the same point of interest and then combining the resulting polynomial models into a single final polynomial. As spurious oscillations are to be avoided near discontinuities and shocks, each polynomial model receives a weight dependent on their oscillating behaviour, hence the name WENO (Weighted Essentially Non-Oscillatory). The regression method used will be the Least-Squares Method as it provides flexibility with unstructured grids. The introductory chapters give a context for this line of high-order schemes (\ref{chapter:introduction}) as well as the necessary theoretical background. These are followed up by a chapter showcasing the implementation of the scheme developed for the uni-dimensional case and the discussion of several test cases and another, with the same structure, regarding the two-dimensional scenario. The concluding chapter discusses the advantages and drawbacks of the developed scheme.