From the 1 of 7 linked papers with an AI index.
7 papers
Exact Total Variation Minimizers as Non-Oscillatory Limiters in High-Order Methods for Conservation Laws
Gabriel P. Langlois, Jerome Darbon, Rongjie Lai +2
The paper introduces a post‑processing step that applies exact total‑variation denoising, computed via a differential inclusion algorithm, to eliminate spurious oscillations in hig…
A positivity preserving and entropy stable nodal discontinuous Galerkin scheme for ideal MHD
Yue Wu, Chi-Wang Shu
Numerically solving magnetohydrodynamic (MHD) equations faces many challenges: avoiding divergence error, maintaining positivity, and satisfying entropy conditions. Among discontin…
LGNO: A Local-Global Neural Operator for Hyperbolic Conservation Laws
Hao Wang, Chi-Wang Shu, Qi Tang
Solutions of hyperbolic conservation laws exhibit both smooth structures across large scales and sharp localized features such as shocks and contact discontinuities, making them di…
Efficient Admissible Set Projection in Optimization-based Invariant-Domain-Preserving Limiters for Ideal MHD
Chen Liu, Chi-Wang Shu, Xiangxiong Zhang
Preserving the admissible set of the ideal magnetohydrodynamics (MHD) equations is important not only for producing physically meaningful numerical solutions, but more importantly…
A Positivity-Preserving Relaxation Algorithm
Thomas Izgin, Hendrik Ranocha, Chi-Wang Shu
We combine Patankar-type methods with suitable relaxation procedures that are capable of ensuring correct dissipation or conservation of functionals such as entropy or energy while…
Efficient optimization-based invariant-domain-preserving limiters in solving gas dynamics equations
Chen Liu, Dionysis Milesis, Chi-Wang Shu +1
We introduce effective splitting methods for implementing optimization-based limiters to enforce the invariant domain in gas dynamics in high order accurate numerical schemes. The…