A hybrid finite-volume reconstruction framework for efficient high-order shock-capturing on unstructured meshes

Abstract

In this paper, we present a multi-dimensional, arbitrary-order hybrid reconstruction framework for compressible flows on unstructured meshes. The proposed method advances state-of-the-art high-resolution schemes by combining the efficiency of linear reconstruction with the robustness of high-order non-oscillatory formulations, activated only where necessary through a novel a priori detection strategy. This approach minimises the use of costly Compact Weighted Essentially Non-Oscillatory (CWENOZ) or Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) reconstructions, thereby substantially reducing computational overhead without compromising accuracy or stability. The framework integrates the strengths of CWENOZ formulations and the Multi-dimensional Optimal Order Detection (MOOD) paradigm, while introducing a redesigned Numerical Admissibility Detector (NAD) that classifies the local flow field in a single step into smooth, weakly non-smooth, and discontinuous regions. 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 scheme near discontinuities. This targeted, a priori allocation preserves high-order accuracy where possible and guarantees non-oscillatory, stable solutions near shocks and strong gradients. The proposed hybrid strategy is implemented within the open-source unstructured finite-volume solver UCNS3D and supports arbitrary-order reconstructions on mixed-element meshes. Comprehensive two- and three-dimensional benchmark tests demonstrate that the method maintains the designed order of accuracy in smooth regions while significantly enhancing robustness in shock-dominated flows. Owing to the reduced frequency of expensive nonlinear reconstructions, the framework achieves up to a 2.5 × speed-up compared to a CWENOZ scheme of the same order in 3D compressible turbulence simulations. Overall, this hybrid framework brings high-order accuracy closer to in industrial-scale CFD simulations through its combination of reduced computational cost, improved robustness, and reliability.