Papers

@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{fernandez-fidalgo_very_2020,

title = {Very high-order method on immersed curved domains for finite difference schemes with regular Cartesian grids},

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

url = {https://www.sciencedirect.com/science/article/pii/S0045782519306747},

doi = {10.1016/j.cma.2019.112782},

issn = {0045-7825},

year  = {2020},

date = {2020-03-01},

urldate = {2026-08-06},

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

volume = {360},

pages = {112782},

abstract = {A new very high-order technique for solving conservation laws with curved boundary domains is proposed. A Finite Difference scheme on Cartesian grids is coupled with an original ghost cell method that provide accurate approximations for smooth solutions. The technology is based on a specific least square method with restrictions that enables to handle general Robin conditions. Several examples in two-dimensional geometries are presented for the unsteady Convection–Diffusion equation and the Euler equations. A fifth-order WENO scheme is employed with matching fifth-order reconstruction at the boundaries. Arbitrary high-order reconstruction for smooth flows is achievable independently of the underlying differential equation since the method works as a black-box dedicated to boundary condition treatment.},

keywords = {Cartesian grids, Compressible flows, Embedded boundary, Finite difference, High-order schemes, ROD},

pubstate = {published},

tppubtype = {article}

}

@article{fernandez-fidalgo_posteriori_2018,

title = {An textita posteriori, efficient, high-spectral resolution hybrid finite-difference method for compressible flows},

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

url = {https://www.sciencedirect.com/science/article/pii/S0045782518300926},

doi = {10.1016/j.cma.2018.02.013},

issn = {0045-7825},

year  = {2018},

date = {2018-06-01},

urldate = {2026-08-04},

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

volume = {335},

pages = {91–127},

abstract = {A high-order hybrid method consisting of a high-accurate explicit finite-difference scheme and a Weighted Essentially Non-Oscillatory (WENO) scheme is proposed in this article. Following this premise, two variants are outlined: a hybrid made up of a Finite Difference scheme and a compact WENO scheme (CRWENO 5), and a hybrid made up of a Finite Difference scheme and a non-compact WENO scheme (WENO 5). The main difference with respect to similar schemes is its a posteriori nature, based on the Multidimensional Optimal Order Detection (MOOD) method. To deal with complex geometries, a multi-block approach using Moving Least Squares (MLS) procedure for communication between meshes is used. The hybrid schemes are validated with several 1D and 2D test cases to illustrate their accuracy and shock-capturing properties.},

keywords = {Compressible flows, Finite differences, High-order schemes, Overset grids},

pubstate = {published},

tppubtype = {article}

}