eMOOD: Entropy-Based Multidimensional Optimal Order Detection for High-Order Shock-Capturing Finite-Volume Schemes
Abstract
We present eMOOD, an entropy-guided evolution of the Multidimensional Optimal Order Detection (MOOD) framework for high-order finite-volume methods on unstructured meshes. A novel troubled-cell indicator based on numerical entropy production replaces the classical relaxed discrete maximum principle. Using entropy generation as a physically motivated measure of non-smoothness, the detector targets shocks, contact discontinuities and under-resolved flow features with a compact stencil. Compared with conventional MOOD detection, eMOOD reduces flagged cells by up to 75%, improving efficiency and reducing memory-access overhead. The detector is used within both the classical MOOD cascade of progressively reduced-order schemes and a novel MOOD-CWENO hybrid, which retains inexpensive linear reconstruction in smooth regions and activates nonlinear high-order reconstruction only where needed. Implemented in the open-source parallel solver UCNS3D, the methodology is assessed on the Shu-Osher shock-entropy-wave interaction, double Mach reflection, supersonic forward-facing step, shock-helium-bubble interaction and triple material point problems. These benchmarks encompass strong shock interactions, shock-induced instabilities, multi-material interfaces and vortex-dominated flows, testing robustness, shock capturing and accuracy on unstructured meshes. Results show that eMOOD preserves the accuracy and robustness of reference CWENO and MOOD formulations while achieving speed-ups of up to 20% without loss of solution quality. Its compact detection stencil, reduced memory footprint and improved localisation offer a more scalable and efficient framework for massively parallel high-order compressible-flow simulations. UK Ministry of Defence (copyright) Crown owned copyright 2026 AWE.
Related
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BibTeX
@misc{uminski2026emood,
title = {{eMOOD: Entropy-Based Multidimensional Optimal Order Detection for High-Order Shock-Capturing Finite-Volume Schemes}},
author = {Michał Umiński and Panagiotis Tsoutsanis and Ahmed A Sheikh Al-Shabab and Alan S. Dawes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20133},
eprint = {2610.20133},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20133},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - eMOOD: Entropy-Based Multidimensional Optimal Order Detection for High-Order Shock-Capturing Finite-Volume Schemes
AU - Michał Umiński
AU - Panagiotis Tsoutsanis
AU - Ahmed A Sheikh Al-Shabab
AU - Alan S. Dawes
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20133
UR - https://arxiv.org/abs/2610.20133
AB - We present eMOOD, an entropy-guided evolution of the Multidimensional Optimal Order Detection (MOOD) framework for high-order finite-volume methods on unstructured meshes. A novel troubled-cell indicator based on numerical entropy production replaces the classical relaxed discrete maximum principle. Using entropy generation as a physically motivated measure of non-smoothness, the detector targets shocks, contact discontinuities and under-resolved flow features with a compact stencil. Compared with conventional MOOD detection, eMOOD reduces flagged cells by up to 75%, improving efficiency and reducing memory-access overhead. The detector is used within both the classical MOOD cascade of progressively reduced-order schemes and a novel MOOD-CWENO hybrid, which retains inexpensive linear reconstruction in smooth regions and activates nonlinear high-order reconstruction only where needed. Implemented in the open-source parallel solver UCNS3D, the methodology is assessed on the Shu-Osher shock-entropy-wave interaction, double Mach reflection, supersonic forward-facing step, shock-helium-bubble interaction and triple material point problems. These benchmarks encompass strong shock interactions, shock-induced instabilities, multi-material interfaces and vortex-dominated flows, testing robustness, shock capturing and accuracy on unstructured meshes. Results show that eMOOD preserves the accuracy and robustness of reference CWENO and MOOD formulations while achieving speed-ups of up to 20% without loss of solution quality. Its compact detection stencil, reduced memory footprint and improved localisation offer a more scalable and efficient framework for massively parallel high-order compressible-flow simulations. UK Ministry of Defence (copyright) Crown owned copyright 2026 AWE.
ER -