Papers

@article{nogueira_machine_2024,

title = {Machine learning-based WENO5 scheme},

author = {Xesús Nogueira-Garea and Javier Fernández-Fidalgo and Lucía Ramos-García and Iván Couceiro-Aguiar and Luis Ramírez-Palacios},

url = {https://www.sciencedirect.com/science/article/pii/S0898122124002505},

doi = {10.1016/j.camwa.2024.05.031},

issn = {0898-1221},

year  = {2024},

date = {2024-08-01},

urldate = {2026-04-21},

journal = {Computers & Mathematics with Applications},

volume = {168},

pages = {84–99},

abstract = {Machine learning (ML) is becoming a powerful tool in Computational Fluid Dynamics (CFD) to enhance the accuracy, efficiency, and automation of simulations. Currently, in the design of shock-capturing methods, there is still a heavy reliance on the expertise and scientific knowledge of each author, particularly in nonlinear components such as smoothness indicators and weighting functions. ML has the potential to reduce this dependency, since by leveraging large datasets, they can learn intricate patterns and make accurate predictions of these functions. In this work we present a neural network that compute the weighting functions in the WENO5 scheme. The proposed WENO5-NN scheme generalizes well for different resolutions, and in most of the cases tested, it outperforms the classical WENO5-JS scheme.},

keywords = {Euler equations, Finite difference, machine learning, Neural networks, WENO},

pubstate = {published},

tppubtype = {article}

}

@article{fernandez-fidalgo_reduced-dissipation_2021,

title = {A reduced-dissipation WENO scheme with automatic dissipation adjustment},

author = {Javier Fernández-Fidalgo and Luis Ramírez-Palacios and Panagiotis Tsoutsanis and Ignasi Colominas-Ezponda and Xesús Nogueira-Garea},

url = {https://www.sciencedirect.com/science/article/pii/S0021999120305234},

doi = {10.1016/j.jcp.2020.109749},

issn = {0021-9991},

year  = {2021},

date = {2021-01-01},

urldate = {2026-08-06},

journal = {Journal of Computational Physics},

volume = {425},

pages = {109749},

abstract = {In this paper, we propose a novel modification to the WENO-family schemes to reduce its intrinsic dissipation. In this work, we focus on the WENO5 scheme, which is rewritten in terms of a central plus a dissipative part, and then, the dissipation is controlled based on the flow physics. This is achieved by using the automatic dissipation adjustment (ADA) method in an a posteriori approach. This methodology allows us to greatly increase the accuracy of the original scheme at the same time ensure the robustness of the numerical method. The accuracy and robustness of the proposed scheme are tested by several selected numerical benchmarks.},

keywords = {Adaptive dissipation, Compressible flows, High-order schemes, WENO},

pubstate = {published},

tppubtype = {article}

}

@article{farmakis_weno_2020,

title = {WENO schemes on unstructured meshes using a relaxed textita posteriori MOOD limiting approach},

author = {Pericles S. Farmakis and Panagiotis Tsoutsanis and Xesús Nogueira-Garea},

url = {https://www.sciencedirect.com/science/article/pii/S0045782520301043},

doi = {10.1016/j.cma.2020.112921},

issn = {0045-7825},

year  = {2020},

date = {2020-05-01},

urldate = {2026-08-06},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {363},

pages = {112921},

abstract = {In this paper a relaxed formulation of the a posteriori Multi-dimensional Optimal Order Detection (MOOD) limiting approach is introduced for weighted essentially non-oscillatory (WENO) finite volume schemes on unstructured meshes. The main goal is to minimise the computational footprint of the MOOD limiting approach by employing WENO schemes—by virtue of requiring a smaller number of cells to reduce their order of accuracy compared to an unlimited scheme. The key characteristic of the present relaxed MOOD formulation is that the Numerical Admissible Detector (NAD) is not uniquely defined for all orders of spatial accuracy, and it is relaxed when reaching a 2nd-order of accuracy. The augmented numerical schemes are applied to the 2D unsteady Euler equations for a multitude of test problems including the 2D vortex evolution, cylindrical explosion, double-Mach reflection, and an implosion. It is observed that in many events, the implemented MOOD paradigm manages to preserve symmetry of the forming structures in simulations, an improvement comparing to the non-MOOD limited counterparts which cannot be easily obtained due to the multi-dimensional reconstruction nature of the schemes.},

keywords = {MOOD, RMI, UCNS3D, Unstructured, WENO},

pubstate = {published},

tppubtype = {article}

}