4 papers
Targeted Entropy-Stable Nonlinear Artificial Dissipation for High-Order Spectral-Element Summation-By-Parts Discretizations
Zelalem Arega Worku, Alex Bercik, David C. Del Rey Fernández +1
Artificial dissipation improves the robustness of high-order methods for under-resolved flows, but can compromise accuracy and suppress physically relevant structures if its streng…
Construction and Optimization of Summation-by-Parts Operators for General Function Spaces Using an Improved Generalized Gaussian Quadrature Algorithm
Alex Bercik, Lisa Patrascu, David W. Zingg
We construct optimized summation-by-parts (SBP) operators for general function spaces with provably minimal degrees of freedom on open, closed, and half-open nodal distributions. T…
On the Practical Impact of Local Linear Instabilities in Entropy-Stable Schemes
Alex Bercik, David W. Zingg
Local linear instability refers to the linearized discrete operator exhibiting perturbation growth exceeding that of the corresponding continuous linearized problem. In the context…
Stable Volume Dissipation for High-Order Finite-Difference and Spectral-Element Methods with the Summation-by-Parts Property
Alex Bercik, David A. Craig Penner, David W. Zingg
The construction of stable, conservative, and accurate volume dissipation is extended to discretizations that possess a generalized summation-by-parts (SBP) property within a tenso…