Agradecimentos: Open access funding provided by Max Planck Society. This work developed during a two-moth stay of the first author at the Max Planck Institute for Mathematics (MPIM) in Bonn during summer of 2017. He would like to express his gratitude for the generous financial support by the MPIM...

Agradecimentos: Open access funding provided by Max Planck Society. This work developed during a two-moth stay of the first author at the Max Planck Institute for Mathematics (MPIM) in Bonn during summer of 2017. He would like to express his gratitude for the generous financial support by the MPIM as well as the warm and inspiring research atmosphere provided by its staff. Further, we would like to thank the anonymous referees for many helpful suggestions

In this work, a novel artificial viscosity method is proposed using smooth and compactly supported viscosities. These are derived by revisiting the widely used piecewise constant artificial viscosity method of Persson and Peraire as well as the piecewise linear refinement of Klockner et al. with...

In this work, a novel artificial viscosity method is proposed using smooth and compactly supported viscosities. These are derived by revisiting the widely used piecewise constant artificial viscosity method of Persson and Peraire as well as the piecewise linear refinement of Klockner et al. with respect to the fundamental design criteria of conservation and entropy stability. Further investigating the method of modal filtering in the process, it is demonstrated that this strategy has inherent shortcomings, which are related to problems of Legendre viscosities to handle shocks near element boundaries. This problem is overcome by introducing certain functions from the fields of robust reprojection and mollifiers as viscosity distributions. To the best of our knowledge, this is proposed for the first time in this work. The resulting C-0(infinity) artificial viscosity method is demonstrated to provide sharper profiles, steeper gradients, and a higher resolution of small-scale features while still maintaining stability of the method

Fechado