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Nowadays, advances in engineering and CFD have led us to face problems with more complex geometries and higher accuracy needs. Mesh-based and meshless discretizations are usually considered as two completely different strategies to solve partial differential equations, and each comes with its own advantages and disadvantages. Traditionally, mesh – based methods have been employed to solve this CFD problems, but with today’s computational facilities, meshless methods have become very popular for dealing with large deformation or complex geometries problems, like free-surface or wave breaking problems.
In this work, t a high-accurate, stable and low-dissipative meshless method for CFD applications is presented, the MLS-SPH-ALE method. This method can be seen as a generalized meshless method that under certain circumstances and parameters recovers other well-known methods, such as the Smoothed Particle Hydrodynamics method (SPH). Moreover, there is a relation between the MLS-SPH-ALE method and the finite volume method. The method was developed to overcome some of the grand challenges of traditional Lagrangian SPH methods, like boundary conditions, accuracy and the treatment of the free surface.
Luis Ramirez
Associate Professor, University of A Coruna