Eirís, AntonioRamírez, LuisCouceiro, IvánFernández-Fidalgo, JavierParís, JoséNogueira, Xesús2023-12-292023-12-292023Eirís, A., Ramírez, L., Couceiro, I. et al. MLS-SPH-ALE: A Review of Meshless-FV Methods and a Unifying Formulation for Particle Discretizations. Arch Computat Methods Eng 30, 4959–4981 (2023). https://doi.org/10.1007/s11831-023-09965-2http://hdl.handle.net/2183/34722Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.[Abstract:] Mesh-based and particle methods were conceived as two different discretization strategies to solve partial differential equations. In the last two decades computational methods have diversified and a myriad of hybrid formulations that combine elements of these two approaches have been developed to solve Computational fluid dynamics problems. In this work we present a review about the meshless-FV family of methods, an analysis is carried out showing that the MLS-SPH-ALE method can be considered as a general formulation from which a set of particle-based methods can be recovered. Moreover, we show the relations between the MLS-SPH-ALE method and the finite volume method. The MLS-SPH-ALE method is a versatile particle-based method that was developed to circumvent the consistency issues of particle methods caused by the use of the kernel approximation. The MLS-SPH-ALE method is developed from the differential equation in ALE form using the partition unity property which is automatically fulfilled by the Moving Least Squares approximation.engAtribución 3.0 Españahttp://creativecommons.org/licenses/by/3.0/es/Mesh-based methodParticle methodPartial differential equationsComputational methodsComputational fluid dynamics problemsMLS-SPH-ALE methodFinite volume methodKernel approximationMoving least squares approximationjournal articleopen access10.1007/s11831-023-09965-2