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.

翻译：本文融合高阶紧凑近似泰勒（Compact Approximate Taylor, CAT）数值方法与后验多维最优阶检测（Multi-dimensional Optimal Order Detection, MOOD）范型，用于求解双曲型守恒律方程组。所提方法对光滑解具有高精度，对间断解具有本质无震荡特性，并近乎具备万无一失的正性保持能力。文中展示了标量守恒律与守恒律方程组的数值结果，以验证CAT-MOOD方法的恰当行为。