Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Stability and Order of Accuracy Analysis of High-Order Schemes Formulated Using the Flux Reconstruction Approach
Submission Author:
Frederico Bolsoni Oliveira , SP
Co-Authors:
Frederico Bolsoni Oliveira, João Luiz F. Azevedo
Presenter: Frederico Bolsoni Oliveira
doi://10.26678/ABCM.COBEM2021.COB2021-0112
Abstract
A stability analysis is performed on high-order schemes formulated using the Flux Reconstruction (FR) approach. The one-dimensional advection model equation is used for the assessment of the stability region of these schemes when coupled with Runge-Kutta-type time-march procedures. Schemes are created using different numbers of internal points for each cell of the discrete domain, in such a way that a broad spectrum of spatial discretization orders can be analyzed. Multiple correction functions are employed so that well-known schemes, for instance the Discontinuous Galerkin (DG) and the Staggered-Grid schemes, may also be included in the study. The stability analysis is performed by identifying the behavior, in the complex plane, of the eigenvalues associated with each one of the considered cases. It is observed that, as the order of the scheme increases, a significant decrease in its domain of stability occurs, followed by a significant reduction in the amount of artificial dissipation being introduced to the solution.
Keywords
Computational Fluid Dynamics, High-Order Schemes, Flux Reconstruction, stability analysis, Advection Equation
