We present a multi-dimensional, arbitrary-order hybrid reconstruction framework for compressible flows on unstructured meshes. The method advances high-resolution schemes by combining the efficiency of linear reconstruction with the robustness of nonlinear formulations, activated only when needed through a novel a priori detection strategy. This minimizes the use of costly Compact Weighted Essentially Non-Oscillatory (CWENOZ) or Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) reconstructions, reducing computational cost without compromising accuracy or stability. The framework merges CWENOZ and the Multi-dimensional Optimal Order Detection (MOOD) paradigm while introducing a redesigned Numerical Admissibility Detector (NAD) that classifies the local flow into smooth, weakly non-smooth, and discontinuous regions in a single step. Each region is then reconstructed using an optimal method: a high-order linear scheme in smooth areas, CWENOZ in weakly non-smooth zones, and a second-order MUSCL near discontinuities. This targeted a priori allocation preserves high-order accuracy where possible and ensures stable, non-oscillatory behavior near shocks and steep gradients. Implemented within the open-source unstructured finite-volume solver UCNS3D, the framework supports arbitrary-order reconstructions on mixed-element meshes. Extensive two- and three-dimensional benchmarks confirm that it retains the designed accuracy in smooth regions while greatly improving robustness in shock-dominated flows. Thanks to the reduced frequency of nonlinear reconstructions, the method achieves up to 2.5x speed-up over a CWENOZ scheme of equal order in 3D compressible turbulence. This hybrid approach thus brings high-order accuracy closer to industrial-scale CFD through its balance of efficiency, robustness, and reliability.

翻译：我们提出了一种用于非结构网格上可压缩流动的多维任意阶混合重构框架。该方法通过将线性重构的高效性与非线性公式的鲁棒性相结合来推进高分辨率格式，仅当需要时通过一种新颖的先验检测策略激活非线性重构。这最大限度地减少了昂贵的紧致加权本质无振荡（CWENOZ）或守恒律单调上游中心格式（MUSCL）重构的使用，在不牺牲精度或稳定性的前提下降低了计算成本。该框架融合了CWENOZ和多维最优阶检测（MOOD）范式，同时引入了一种重新设计的数值可容许性检测器（NAD），该检测器可在单步内将局部流动分类为光滑、弱非光滑和不连续区域。随后，每个区域采用最优方法进行重构：光滑区域使用高阶线性格式，弱非光滑区域使用CWENOZ，不连续附近使用二阶MUSCL。这种有针对性的先验分配在可能的情况下保持了高阶精度，并确保了在激波和陡峭梯度附近的稳定、无振荡行为。该框架在开源非结构有限体积求解器UCNS3D中实现，支持混合单元网格上的任意阶重构。大量的二维和三维基准测试证实，它在光滑区域保持了设计精度，同时显著提高了激波主导流动中的鲁棒性。由于非线性重构频率的降低，该方法在三维可压缩湍流中相比同阶CWENOZ方案实现了高达2.5倍的加速。因此，这种混合方法通过效率、鲁棒性和可靠性的平衡，使高阶精度更接近工业级计算流体力学应用。