Improvements for accuracy and stability in a weakly-compressible particle method

Two-dimensional continuum modelling granular column collapse by non-local peridynamics in a mesh-free method with rheology

“…The spatial operators are adopted in the framework of the MPS (Koshizuka et al 1998;Gotoh & Khayyer 2016;Xu & Jin 2016a). By using the mesh-free method, the granular material is represented by a set of Lagrangian particles with the same initial distance l, being the continuum-level markers.…”

“…The free surface can be automatically tracked by the mesh-free method (Koshizuka, Nobe & Oka 1998;Shakibaeinia & Jin 2010). The pressure field is determined by an equation of state based on the particle number density (Shakibaeinia & Jin 2010;Xu & Jin 2016a). The μ(I) rheology is applied to calculate the effective viscosity and stress in the granular flow.…”

A numerical and experimental investigation of wave generated by submerged landslides

“…Another model given by the kernel function is the Laplacian model. Originally, it has been introduced from a transient diffusion problem (Batchelor, 1967;Colagrossi and Landrini, 2003;Koshizuka et al, 1998;Koshizuka and Oka, 1996;Xu and Jin, 2016).…”

“…where n* is a temporal particle number density, thus it has been calculated based on the intermediate particle position r* (Koshizuka and Oka, 1996;Lee et al, 2011;Xu and Jin, 2016); c0 is the sound speed, in order to satisfy a compressibility less than 1%, it is given to ten times of the maximum speed in the simulation domain (Koshizuka and Oka, 1996;Shakibaeinia and Jin, 2012b;Tanaka and Masunaga, 2010); =7 is a widely used typical number in MPS method to simulate a weakly compressible flow (Fu and Jin, 2015;Koshizuka and Oka, 1996;Shakibaeinia and Jin, 2009;Xu and Jin, 2016).…”

Simulation of breaking waves on slope beaches integrating the MPS method into Iwagaki wave theory

“…Besides, for a weakly compressible condition, pressure is calculated by a state condition, for the SPH method Monaghan [50], Morris et al [51] and Khayyer and Gotoh [31] and for the MPS method Shakibaeinia and Jin [62]. Moreover, a weakly compressible MPS model has been improved by Xu and Jin [72] considering a Laplacian model in terms of the particle distance, interaction radius and weighting function through a 2D diffusion problem. Furthermore, by a higher-order source term, the corrected incompressible versions of the SPH and MPS methods have been presented to ensure the angular momentum preservation for SPH method, Khayyer et al [34], and for the MPS method by Khayyer and Gotoh [30].…”