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.

翻译：本文将高阶紧凑近似泰勒（CAT）数值格式与后验多维最优阶检测（MOOD）范式相结合，用于求解二维双曲守恒律系统。所得格式在光滑解上具有高精度，在非光滑解上呈现本质无振荡行为，且在正性问题上具备几乎万无一失的特性。通过一组标准测试案例及高难度算例的数值结果验证了CAT-MOOD格式的优异表现。