A Julia library of summation-by-parts (SBP) operators used in finite difference, Fourier pseudospectral, continuous Galerkin, and discontinuous Galerkin methods to get provably stable semidiscretizations, paying special attention to boundary conditions.
The operators described in the arXiv paper are interesting because they modify the boundary closures to guarantee SBP and WENO. The downside is that the paper does not explicitly present the matrices, like Q, in an easy summary for implementation purposes. I am not sure if they fit into the existing method design and data structures herein. However, I would be curious if the modified boundary closures cure and/or alleviate the "hotspots" we have encountered with the 2D Upwind runs for KHI.
ranocha
commented
9 months ago
The operators described in the arXiv paper are interesting because they modify the boundary closures to guarantee SBP and WENO. The downside is that the paper does not explicitly present the matrices, like
Q, in an easy summary for implementation purposes. I am not sure if they fit into the existing method design and data structures herein. However, I would be curious if the modified boundary closures cure and/or alleviate the "hotspots" we have encountered with the 2D Upwind runs for KHI.