A shallow water SPH model with PML boundaries

• Published in: Ocean engineering 2015-11, Vol.108, p.315-324
• Main Authors: Vitanza, Enrico, Grammauta, Rosario, Molteni, Diego, Monteforte, Massimiliano
• Format: Article
• Language: English
• Subjects: Absorbing layer; Absorption; Boundaries; Boundary condition; Computational fluid dynamics; Damping; Fluid mechanics; Lagrangian numerical method; Marine; Mathematical analysis; Mathematical models; Ocean engineering; Shallow water model; SPH; Wave propagation
• ISSN: 0029-8018; 1873-5258
• DOI: 10.1016/j.oceaneng.2015.07.054

We focus on the study and implementation of Smoothed Particle Hydrodynamics (SPH) numerical code to deal with non-reflecting boundary conditions, starting from the Perfect Matched Layer (PML) approach. Basically, the method exploits the concept of a physical damping which acts on a fictitious layer added to the edges of computational domain. In this paper, we develop the study of time dependent shallow waves propagating on a finite 2D-XY plane domain and their behavior in the presence of circular and, more generic, rectangular boundary absorbing layers. In particular, an analysis of variation of the layer׳s thickness versus the absorbing efficiency is conducted. In our model, the magnitude of absorbtion of a specific layer in which two types of damping functions (linear and hyperbolic) are activated is compared with the one produced by the antithetical cases of total reflecting and open boundaries. The results obtained indicate the good applicability of PML approach to SPH numerical scheme showing high absorption values with reasonable thickness of the absorbing layers. •Non-reflecting boundary condition in Lagrangian numerical methods is studied and implemented.•The method is based on the concept of absorbing layer (Perfect Matched Layer method).•We tested its validity and performance for shallow water and for real waves in a two dimensional (XY ) computational domain.