Papers

@article{ait-ali_diffuse_2025,

title = {A Diffuse Interface Model for Cavitation, Taking Into Account Capillary Forces},

author = {Takfarines Ait-Ali and Sofiane Khelladi and Farid Bakir and Noureddine Hannoun and Xesús Nogueira-Garea and Luis Ramírez-Palacios},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.5350},

doi = {10.1002/fld.5350},

issn = {1097-0363},

year  = {2025},

date = {2025-01-01},

urldate = {2026-07-28},

journal = {International Journal for Numerical Methods in Fluids},

volume = {97},

number = {3},

pages = {395–408},

abstract = {We consider the moving least squares method to solve compressible two-phase water-water vapor flow with surface tension. A diffuse interface model based on the Navier–Stokes and Korteweg equations is coupled with a suitable system of state equations that allows for a more realistic estimation of the pressure jump across the liquid–vapor interface as a function of temperature. We propose a simple formulation for computing the capillarity coefficient textbackslash łambda textbackslash based on the surface tension and the thickness of the diffuse interface. A convergence analysis using pressure jump in the test case of static bubble is conducted to verify our solver. We present several numerical test cases that illustrate the ability of our model to reproduce qualitatively and quantitatively the effects of surface tension on cavitation bubbles in general situations.},

note = {_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.5350},

keywords = {cavitation, homogeneous model, hydrodynamics, Korteweg tensor, moving least squares, Surface tension, Tait equation of state for water},

pubstate = {published},

tppubtype = {article}

}

@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{ramirez_arbitrary_2022,

title = {An arbitrary Lagrangian-Eulerian SPH-MLS method for the computation of compressible viscous flows},

author = {Luis Ramírez-Palacios and Antonio Eirís and Iván Couceiro-Aguiar and José París-López and Xesús Nogueira-Garea},

url = {https://www.sciencedirect.com/science/article/pii/S0021999122002340},

doi = {10.1016/j.jcp.2022.111172},

issn = {0021-9991},

year  = {2022},

date = {2022-09-01},

urldate = {2026-08-07},

journal = {Journal of Computational Physics},

volume = {464},

pages = {111172},

abstract = {In this work we present a high-accurate discretization to solve the compressible Navier-Stokes equations using an Arbitrary Lagrangian-Eulerian meshless method (SPH-MLS), which can be seen as a general formulation that includes some well-known meshfree methods as a particular case. The formulation is based on the use of Moving Least Squares (MLS) approximants as weight functions on a Galerkin formulation and to accurate discretize the convective and viscous fluxes. This formulation also verifies the discrete partition of unity and reproduces the zero-gradient condition for constant functions. Convective fluxes are discretized using Riemann solvers. In order to obtain high accuracy MLS is also used for the high-order reconstruction of the Riemann states. The accuracy and performance of the proposed method is demonstrated by solving different steady and unsteady benchmark problems.},

keywords = {Compressible viscous flows, Meshless methods, moving least squares, Navier-Stokes equations, Smoothed Particle Hydrodynamics},

pubstate = {published},

tppubtype = {article}

}

@article{prieto-arranz_well-balanced_2021,

title = {A Well-Balanced SPH-ALE Scheme for Shallow Water Applications},

author = {Alberto Prieto-Arranz and Luis Ramírez-Palacios and Iván Couceiro-Aguiar and Ignasi Colominas-Ezponda and Xesús Nogueira-Garea},

url = {https://doi.org/10.1007/s10915-021-01600-1},

doi = {10.1007/s10915-021-01600-1},

issn = {1573-7691},

year  = {2021},

date = {2021-08-01},

urldate = {2026-08-07},

journal = {Journal of Scientific Computing},

volume = {88},

number = {3},

pages = {84},

abstract = {In this work, a new discretization of the source term of the shallow water equations with non-flat bottom geometry is proposed to obtain a well-balanced scheme. A Smoothed Particle Hydrodynamics Arbitrary Lagrangian-Eulerian formulation based on Riemann solvers is presented to solve the SWE. Moving-Least Squares approximations are used to compute high-order reconstructions of the numerical fluxes and, stability is achieved using the a posteriori MOOD paradigm. Several benchmark 1D and 2D numerical problems are considered to test and validate the properties and behavior of the presented schemes.},

keywords = {moving least squares, shallow water equations, Smoothed Particle Hydrodynamics, SPH-ALE, Well-balanced methods},

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{ramirez_very_2018,

title = {A very accurate Arbitrary Lagrangian–Eulerian meshless method for Computational Aeroacoustics},

author = {Luis Ramírez-Palacios and Xesús Nogueira-Garea and Sofiane Khelladi and Abdelkader Krimi and Ignasi Colominas-Ezponda},

url = {https://www.sciencedirect.com/science/article/pii/S0045782518303694},

doi = {10.1016/j.cma.2018.07.036},

issn = {0045-7825},

year  = {2018},

date = {2018-12-01},

urldate = {2026-08-04},

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

volume = {342},

pages = {116–141},

abstract = {In this work, we propose a new meshless approach based on a Galerkin discretization of a set of conservation equations on an Arbitrary Lagrangian–Eulerian framework. In particular, we solve the Linearized Euler Equations, using Moving Least Squares as weight functions in the Galerkin discretization. Riemann solvers are introduced in the formulation for the discretization of the convective fluxes. Differently from a purely Lagrangian approach, as it is usual in SPH, the present method is able to work in both Eulerian and Lagrangian configurations, which allows using all the advantages of the Lagrangian approaches in the context of Computational Aeroacoustics.},

keywords = {Computational aeroacoustics, Meshless methods, moving least squares, Smoothed Particle Hydrodynamics},

pubstate = {published},

tppubtype = {article}

}