A Hybrid Reconstruction Framework for Efficient High-Order Shock-Capturing on Unstructured Meshes

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.