An almost fail-safe a-posteriori limited high-order CAT scheme

TL;DR

This paper introduces a high-order numerical scheme combining CAT and MOOD methods for 2D hyperbolic conservation laws, achieving high accuracy, non-oscillatory behavior, and near fail-safe positivity.

Contribution

The paper presents a novel blend of high-order CAT schemes with an a-posteriori MOOD paradigm, enhancing stability and accuracy for complex 2D hyperbolic problems.

Findings

High accuracy on smooth solutions

Non-oscillatory behavior on irregular solutions

Near fail-safe positivity preservation

Abstract

In this paper we blend the high order Compact Approximate Taylor (CAT) numerical schemes with an a-posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm to solve hyperbolic systems of conservation laws in 2D. The resulting scheme presents high accuracy on smooth solutions, essentially non-oscillatory behavior on irregular ones, and, almost fail-safe property concerning positivity issues. The numerical results on a set of sanity test cases and demanding ones are presented assessing the appropriate behavior of the CAT-MOOD scheme.