In this paper we blend high-order Compact Approximate Taylor (CAT) numerical methods with the a posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm to solve hyperbolic systems of conservation laws. The resulting methods are highly accurate for smooth solutions, essentially non-oscillatory for discontinuous ones, and almost fail-safe positivity preserving. Some numerical results for scalar conservation laws and systems are presented to show the appropriate behavior of CAT-MOOD methods.
@article{arxiv.2303.11391,
title = {CAT-MOOD methods for conservation laws in one space dimension},
author = {R. Loubere and E. Macca and C. Pares and G. Russo},
journal= {arXiv preprint arXiv:2303.11391},
year = {2023}
}