Papers

@article{ramirez_new_2023,

title = {A new Mean Preserving Moving Least Squares method for Arbitrary Order Finite Volume schemes},

author = {Luis Ramírez-Palacios and Laura Edreira-Marzoa and Iván Couceiro-Aguiar and Pablo Ouro and Xesús Nogueira-Garea and Ignasi Colominas-Ezponda},

url = {https://www.sciencedirect.com/science/article/pii/S0096300322008360},

doi = {10.1016/j.amc.2022.127768},

issn = {0096-3003},

year  = {2023},

date = {2023-04-01},

urldate = {2026-08-07},

journal = {Applied Mathematics and Computation},

volume = {443},

pages = {127768},

abstract = {In this paper we propose a new arbitrary-order Finite Volume method for the numerical solution of the Euler and Navier-Stokes equations on unstructured grids. Arbitrary order is achieved using a modified Moving Least Squares reconstruction, which preserves the mean values of the conservative variables. Hence, the proposed scheme changes the traditional error functional of the MLS reconstruction in order to compare the cell-averaged values. Several benchmark problems are used to assess the proposed scheme’s accuracy and performance, to show that arbitrary order of convergence can be achieved. Furthermore, the proposed method is applied to the numerical solution of the Navier-Stokes equations and its ability to simulate turbulent flows is verified.},

keywords = {Compressible flows, Finite volume, Mean Preserving, moving least squares, Very high-order methods},

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{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{nogueira_posteriori-implicit_2020,

title = {An a posteriori-implicit turbulent model with automatic dissipation adjustment for Large Eddy Simulation of compressible flows},

author = {Xesús Nogueira-Garea and Luis Ramírez-Palacios and Javier Fernández-Fidalgo and Michael Deligant and Sofiane Khelladi and Jean-Camille Chassaing and Fermín Navarrina-Martínez},

url = {https://www.sciencedirect.com/science/article/pii/S0045793019303147},

doi = {10.1016/j.compfluid.2019.104371},

issn = {0045-7930},

year  = {2020},

date = {2020-01-01},

urldate = {2026-08-06},

journal = {Computers & Fluids},

volume = {197},

pages = {104371},

abstract = {In this work we present an a posteriori high-order finite volume scheme for the computation of compressible turbulent flows. An automatic dissipation adjustment (ADA) method is combined with the a posteriori paradigm, in order to obtain an implicit subgrid scale model and preserve the stability of the numerical method. Thus, the numerical scheme is designed to increase the dissipation in the control volumes where the flow is under-resolved, and to decrease the dissipation in those cells where there is excessive dissipation. This is achieved by adding a multiplicative factor to the dissipative part of the numerical flux. In order to keep the stability of the numerical scheme, the a posteriori approach is used. It allows to increase the dissipation quickly in cells near shocks if required, ensuring the stability of the scheme. Some numerical tests are performed to highlight the accuracy and robustness of the proposed numerical scheme.},

keywords = {A posteriori shock capturing, Compressible flows, Computational fluid dynamics, High-order methods, Implicit large eddy simulation},

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}

}