A WCSPH Particle Shifting Strategy for Simulating Violent Free Surface Flows

Abstract

In this work, we develop an enhanced particle shifting strategy in the framework of weakly compressible δ+-SPH method. This technique can be considered as an extension of the so-called improved particle shifting technology (IPST) proposed by Wang et al. (2019). We introduce a new parameter named “ϕ” to the particle shifting formulation, on the one hand to reduce the effect of truncated kernel support on the formulation near the free surface region, on the other hand, to deal with the problem of poor estimation of free surface particles. We define a simple criterion based on the estimation of particle concentration to limit the error’s accumulation in time caused by the shifting in order to achieve a long time violent free surface flows simulation. We propose also an efficient and simple concept for free surface particles detection. A validation of accuracy, stability and consistency of the presented model was shown via several challenging benchmarks.

A Review of SPH Techniques for Hydrodynamic Simulations of Ocean Energy Devices

“…Notwithstanding, it should be underlined that although the original version of PST and its variants show remarkable ability to cope with several challenging problems, their physical rationality could pose some limitations when being applied to realistic engineering problems. For instance, as reported by the extensive SPH literature (see, e.g., [155,157,158,160]), several versions of PST (see, e.g., [118,156]) could trigger the volume-non-conservation issue in simulating violent free-surface flows with long-term duration. This is caused by the fact that in these PST variants, after being repositioned, the particle positions are still updated according to an unchanged velocity field (i.e., non-Lagrangian transport velocity), which is nonphysical from a rigorous point of view.…”

“…After this pioneering work, PST has been further developed by the SPH community and applied to diverse problems, forming various PST variants in both the weakly compressible and truly incompressible senses (see e.g., [93,118,148,[151][152][153][154][155][156][157][158][159]). It is undeniable that PSTs can offer uniform particle distribution (i.e., better quality of particle distribution-see also Figure 10) and thus improve the numerical accuracy and stability of SPH simulations.…”

“…Therefore, the SPH community have been struggling for making PST more physical in different ways, such as integrating the shifting velocity, δv, into the governing equations (see, e.g., [155,158]) and using a fully Arbitrary-Lagrangian-Eulerian (ALE) framework (see, e.g., [148,161]); these variants strongly improve the rationality and interpretability of PSTs through rigorous mathematical considerations, although they require modifying the existing codes to a large extent because of the more complex formalism of the governing equations. In addition to that, there have been simpler measures such as locally deactivating shifting when the fluid suffers from the volume-non-conservation issue [157] or introducing a corrective cohesion force to adaptively compensate the over-expansion/compression [160]. On the whole, as a simple and powerful SPH technique, PSTs should be taken into account for simulating OEDs to improve the accuracy and stability of the simulation.…”

Enhanced weakly-compressible MPS method for violent free-surface flows: Role of particle regularization techniques

“…Nevertheless, despite their success in improving the particle distributions, many existing particle-shifting methods and the associated free-surface detection algorithms introduce some new challenges in simulating such complex flows (e.g., [6,14]). Particularly in weakly compressible particle methods, where the potential energy is dominant and several breaking events occur (e.g., water dam break and sloshing problems), the continuous shifting of the particles leads to an unphysical expansion of the fluid field [5,32]. Further developments to overcome these numerical issues involve implementing more accurate particle classification algorithms and treatment of the free-surface particles (e.g., [6,25,32]).…”

“…Particularly in weakly compressible particle methods, where the potential energy is dominant and several breaking events occur (e.g., water dam break and sloshing problems), the continuous shifting of the particles leads to an unphysical expansion of the fluid field [5,32]. Further developments to overcome these numerical issues involve implementing more accurate particle classification algorithms and treatment of the free-surface particles (e.g., [6,25,32]).…”