MLS-SPH-ALE: A Review of Meshless-FV Methods and a Unifying Formulation for Particle Discretizations

• Published in: Archives of computational methods in engineering Vol. 30; no. 8; pp. 4959 - 4981
• Main Authors: Eirís, Antonio, Ramírez, Luis, Couceiro, Iván, Fernández-Fidalgo, Javier, París, José, Nogueira, Xesús
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.11.2023; Springer Nature B.V
• Subjects: Approximation; Computational fluid dynamics; Engineering; Finite volume method; Mathematical analysis; Mathematical and Computational Engineering; Meshless methods; Partial differential equations; Particle methods (mathematics); Review Article
• ISSN: 1134-3060; 1886-1784
• DOI: 10.1007/s11831-023-09965-2

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.