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In this paper we blend the high order Compact Approximate Taylor (CAT)numerical schemes with an a-posteriori Multi-dimensional Optimal OrderDetection (MOOD) paradigm to solve hyperbolic systems of conservation laws in2D. The resulting scheme presents high accuracy on smooth solutions,essentially non-oscillatory behavior on irregular ones, and, almost fail-safeproperty concerning positivity issues. The numerical results on a set of sanitytest cases and demanding ones are presented assessing the appropriate behaviorof the CAT-MOOD scheme.

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