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

TL;DR

This paper introduces a hybrid reconstruction framework for unstructured mesh CFD that combines high-order accuracy with robustness near shocks, significantly reducing computational costs while maintaining solution quality.

Contribution

The novel framework integrates a flow classification strategy with adaptive reconstruction, minimizing costly nonlinear schemes and enabling efficient high-order shock-capturing on unstructured meshes.

Findings

Achieves up to 2.5x speed-up compared to traditional CWENOZ reconstructions.

Maintains high-order accuracy in smooth regions and robustness near shocks.

Validated on 2D and 3D benchmarks with improved efficiency.

Abstract

In this paper, we present a multi-dimensional, arbitrary-order hybrid reconstruction framework for compressible flows on unstructured meshes. The method combines the efficiency of linear reconstruction with the robustness of high-order non-oscillatory schemes, activated only where needed through a novel a priori detection strategy. By minimising the use of costly CWENOZ and MUSCL reconstructions, the approach substantially reduces computational expense without sacrificing accuracy or stability. The framework blends CWENOZ formulations with the MOOD paradigm and introduces a redesigned Numerical Admissibility Detector that classifies the flow in a single step as smooth, weakly non-smooth, or discontinuous. Smooth regions use high-order linear reconstruction, weakly non-smooth regions use CWENOZ, and discontinuities are treated with second-order MUSCL. This targeted allocation preserves high-order accuracy while ensuring non-oscillatory and stable solutions near shocks. Implemented in the open-source unstructured finite-volume solver UCNS3D, the method supports arbitrary-order reconstruction on mixed-element meshes. Two- and three-dimensional benchmarks confirm the designed accuracy in smooth regions and enhanced robustness in shock-dominated flows. Reduced reliance on nonlinear reconstructions yields up to a 2.5x speed-up over same-order CWENOZ in 3D compressible turbulence simulations, bringing high-order accuracy closer to industrial-scale CFD applications.