Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902626 | Applied Numerical Mathematics | 2018 | 23 Pages |
Abstract
The flux reconstruction is a framework of high order semidiscretisations used for the numerical solution of hyperbolic conservation laws. Using a reformulation of these schemes relying on summation-by-parts (SBP) operators and simultaneous approximation terms, artificial dissipation/spectral viscosity operators and connections to modal filtering are investigated. Firstly, the discrete viscosity operators are studied for general SBP bases, stressing the importance of the correct implementation in order to get both conservative and stable approximations. Starting from L2 stability for scalar conservation laws, the results are extended to entropy stability for hyperbolic systems and supported by numerical experiments. Furthermore, the relation to modal filtering is recalled and several possibilities to apply filters are investigated, both analytically and numerically. This analysis serves to single out a unique way to apply modal filters in numerical methods.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Hendrik Ranocha, Jan Glaubitz, Philipp Ãffner, Thomas Sonar,