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CAT-MOOD methods for conservation laws in one space dimension (2303.11391v1)
Published 20 Mar 2023 in math.NA and cs.NA
Abstract: 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.