Papers

@article{ramirez_very_2025,

title = {A very fast high-order flux reconstruction for Finite Volume schemes for Computational Aeroacoustics},

author = {Luis Ramírez-Palacios and Javier Fernández-Fidalgo and José París-López and Michael Deligant and Sofiane Khelladi and Xesús Nogueira-Garea},

url = {https://doi.org/10.1007/s00366-024-02039-2},

doi = {10.1007/s00366-024-02039-2},

issn = {1435-5663},

year  = {2025},

date = {2025-02-01},

urldate = {2026-04-28},

journal = {Engineering with Computers},

volume = {41},

number = {1},

pages = {667–680},

abstract = {Given the small wavelengths and wide range of frequencies of the acoustic waves involved in Aeroacoustics problems, the use of very accurate, low-dissipative numerical schemes is the only valid option to accurately capture these phenomena. However, as the order of the scheme increases, the computational time also increases. In this work, we propose a new high-order flux reconstruction in the framework of finite volume (FV) schemes for linear problems. In particular, it is applied to solve the Linearized Euler Equations, which are widely used in the field of Computational Aeroacoustics. This new reconstruction is very efficient and well suited in the context of very high-order FV schemes, where the computation of high-order flux integrals are needed at cell edges/faces. Different benchmark test cases are carried out to analyze the accuracy and the efficiency of the proposed flux reconstruction. The proposed methodology preserves the accuracy while the computational time relatively reduces drastically as the order increases.},

keywords = {Computational aeroacoustics, Finite volume, High-order methods, Mean preserving moving least squares},

pubstate = {published},

tppubtype = {article}

}

@article{eiris_sph-ale_2021,

title = {SPH-ALE Scheme for Weakly Compressible Viscous Flow with a Posteriori Stabilization},

author = {Antonio Eirís and Luis Ramírez-Palacios and Javier Fernández-Fidalgo and Iván Couceiro-Aguiar and Xesús Nogueira-Garea},

url = {https://www.mdpi.com/2073-4441/13/3/245},

doi = {10.3390/w13030245},

issn = {2073-4441},

year  = {2021},

date = {2021-01-01},

urldate = {2026-08-07},

journal = {Water},

volume = {13},

number = {3},

pages = {245},

publisher = {Multidisciplinary Digital Publishing Institute},

abstract = {A highly accurate SPH method with a new stabilization paradigm has been introduced by the authors in a recent paper aimed to solve Euler equations for ideal gases. We present here the extension of the method to viscous incompressible flow. Incompressibility is tackled assuming a weakly compressible approach. The method adopts the SPH-ALE framework and improves accuracy by taking high-order variable reconstruction of the Riemann states at the midpoints between interacting particles. The moving least squares technique is used to estimate the derivatives required for the Taylor approximations for convective fluxes, and also provides the derivatives needed to discretize the viscous flux terms. Stability is preserved by implementing the a posteriori Multi-dimensional Optimal Order Detection (MOOD) method procedure thus avoiding the utilization of any slope/flux limiter or artificial viscosity. The capabilities of the method are illustrated by solving one- and two-dimensional Riemann problems and benchmark cases. The proposed methodology shows improvements in accuracy in the Riemann problems and does not require any parameter calibration. In addition, the method is extended to the solution of viscous flow and results are validated with the analytical Taylor–Green, Couette and Poiseuille flows, and lid-driven cavity test cases.},

keywords = {High-order methods, Meshless methods, moving least squares, Multi-dimensional Optimal Order Detection, Smoothed Particle Hydrodynamics, weakly compressible},

pubstate = {published},

tppubtype = {article}

}

@article{martinez_high-order_2020,

title = {A high-order finite volume method with improved isotherms reconstruction for the computation of multiphase flows using the Navier–Stokes–Korteweg equations},

author = {Abel Martínez and Luis Ramírez-Palacios and Xesús Nogueira-Garea and Sofiane Khelladi and Fermín Navarrina-Martínez},

url = {https://www.sciencedirect.com/science/article/pii/S0898122119303736},

doi = {10.1016/j.camwa.2019.07.021},

issn = {0898-1221},

year  = {2020},

date = {2020-02-01},

urldate = {2026-08-06},

journal = {Computers & Mathematics with Applications},

volume = {79},

number = {3},

pages = {673–696},

abstract = {In this work we solve the Navier–Stokes–Korteweg (NSK) equations to simulate a two-phase fluid with phase change. We use these equations on a diffuse interface approach, where the properties of the fluid vary continuously across the interface that separates the different phases. The model is able to describe the behavior of both phases with the same set of equations, and it is also able to handle problems with great changes in the topology of the problem. However, high-order derivatives are present in NSK equations, which is a difficulty for the design of a numerical method to solve the problem. Here, we propose the use of a high-order Finite Volume method with Moving Least Squares approximations to handle high-order derivatives and solve the NSK equations. Moreover, a new methodology to obtain accurate equations of state is presented. In this method, we use any accurate equation of state for the pure phases. Under the saturation curve, a B-spline reconstruction fulfilling a given set of thermodynamic criteria is performed. The new EOS can be used for computations using diffuse interface modeling. Several numerical examples to show the accuracy of the new approach are presented.},

keywords = {Diffuse interface, Finite volume, High-order methods, moving least squares, Phase transition},

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}

}