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With the increasing demand of large scale computation, multi-resolution particle methods have been paid much attention by many researchers. In multi-resolution method, high resolution is applied in local area to reduce the whole computational costs and maintain the local accuracy. However, there are still many challenges in the stability and accuracy of multi-resolution particle methods. In this research, an efficient variable particle size (VSP) multi-resolution method, using particle splitting and coalescing techniques, is developed in moving semi-implicit particle (MPS) method. Particles split or coalesce in dynamic five steps to avoid particle overlap and clustering. The mixed splitting mechanism by combining hexagonal splitting pattern and pair splitting pattern are proposed in the five-step splitting algorithm. Pair splitting and coalescing techniques with variable particle size are proposed to strictly ensure the conservation of mass and momentum and avoid particle clustering. To solve the non-linear fluid-structure interaction problem, the VSP algorithm is introduced in MPS-DEM method. The numerical results are compared with the analytical solutions and experimental results. It shows that the proposed VSP algorithm cannot only maintain the local accuracy, but also improve the computational efficiency by avoiding unnecessary chain operations between particle splitting and coalescing. [ABSTRACT FROM AUTHOR]

• The shape and position of the high-resolution domains were able to dynamically trace the moving/deformable body with mass and momentum conservation. • The particle size is not unique but a range for each resolution domains, and the principle of resolution selection between neighboring domains is optimized. • New splitting/coalescing criterion is proposed to avoid chain split/coalesce reaction, and to improve the convergence near the multi-resolution boundaries. • The AVSP-MPS method sharply reduces the particle number and the computational time. For the single-resolution particle method, large computation demand with high accuracy commonly requires enormous number of particles, which becomes greatly time-consuming. The moving particle semi-implicit (MPS) method with variable-size particles (VSP) has been proposed to refine particles in local domain. However, in VSP-MPS method, the refined area is fixed in the calculation, which makes it difficult to precisely capture flow near moving and deformable boundaries. This study develops a MPS method with adaptive variable-size particles model, called AVSP-MPS. In this method, by capturing moving and deformable boundaries, the objective computational domain can be dynamically refined. A new criterion, that splitting and coalescing only happen when the entire particle crosses the refined interface, is proposed to avoid unnecessary chain reactions of particle splitting and coalescing. The stability of the method is therefore improved. The district resolution is not a specific value, but a range in VSP model. An inappropriate selection of resolution range would cause repetitive splitting and coalescing, leading to low efficiency of the computation. In this research, the new maximum and minimum volumes in the region with different resolutions, as an optimized result, are obtained to improve convergence near the multi-resolution boundaries. Several cases as dam break and water entry are verified. The numerical results show that the AVSP-MPS method has an efficient, flexible and stable refinement technique in treating complex flow with large deformation. [ABSTRACT FROM AUTHOR]

• A fully lagrangian meshfree implicit structure model is developed with three novel schemes (HT-PC-HD). • HT; High-order implicit time integration for update of particles' velocities and positions. • PC; predictor-corrector method for estimation of rotation matrix. • HD; High-order discretization operator models for deformation gradient and acceleration by elastic force. • The implicit structure model and integrated FSI solver are shown to have good accuracy and stability. In this paper, a novel SPH (Smoothed Particle Hydrodynamics)-based implicit structure model as well as its refined coupled fully-Lagrangian meshfree FSI (Fluid-Structure Interaction) solver are presented. The implicit structure model is founded through consideration of conservation law of linear momentum. The implicit time integration is achieved along with the assumption of linear elastic material. For development of refined implicit structure model, three novel schemes are considered; (1) High-order implicit Time integration (HT) scheme is considered for enhanced implicit update of particles' velocities and positions; (2) Predictor-Corrector (PC) method is incorporated for improved estimation of rotation matrix; (3) High-order Discretization (HD) operator is employed for consistent calculation of deformation gradient and acceleration by elastic force. The proposed SPH-based implicit structure model is coupled with a refined ISPH fluid model so as to develop an enhanced fully-Lagrangian meshfree FSI solver, where consistent time coupling between incompressible fluid flow and stiff structures can be achieved by using the same time step sizes in both phases. The proposed implicit structure model as well as its corresponding FSI solver are verified in terms of robustness and accuracy by reproducing a set of well-known benchmark tests. [Display omitted] [ABSTRACT FROM AUTHOR]

• Unstable pressure computation investigated from a totally new viewpoint of particle-level contact/collisions. • Proposition of correction based on momentum conservation of particle-level collisions. • New stable source terms are derived for pressure Poisson equation (PPE), mitigating pressure oscillations in a wider range of time and spatial resolutions. • Very simple implementation and no additional computational effort, which are desirable for practical engineering applications. • The approach can be combined with other strategies and incorporate into other projected-based particle methods. • Extensive verifications through hydrostatic and hydrodynamic benchmarks. The aim of this paper is to investigate the unstable nature of pressure computation focusing on incompressible flow modeling through the projection-based particle methods. A new approach from the original viewpoint of the momentum conservation regarding particle-level collisions, hereinafter refered to as time-scale correction of particle-level impulses (TCPI), is proposed to derive new source terms of pressure Poisson equation (PPE). This results in more stable computations with drastic reduction of unphysical pressure oscillations and more robust simulation with pressure magnitudes almost independent to time step. Moreover, compared to other strategies, no additional computational effort is required, its implementation is extremely simple, and the only numerical parameter is the propagation speed of the perturbations, of which the calibration is much more straightforward due to its physical meaning. Simulations were carried out using moving particle semi-implicit (MPS) method improved by the proposed approach. The comparisons of computed results with theoretical and experimental ones confirmed the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Lagrangian particle methods such as smoothed particle hydrodynamics (SPH) and the finite volume particle method (FVPM) can suffer from non-physical voids in the spatial discretisation, due to the inability of numerical particles to deform as continuum fluid elements can. It is known that the situation can be improved for wall-bounded flows in SPH by adding a uniform background pressure to ensure positive absolute pressure everywhere. In this article, we investigate the application of background pressure in FVPM, and show that numerical voids grow under negative pressure and collapse under positive pressure. To use this technique in free-surface flow, however, the background pressure must be applied as an atmospheric pressure at the free surface. A kinematic criterion for free surface extension (KCFSE) to differentiate physical free surfaces from new numerical voids has been developed, supplementing the inherent capability of FVPM to identify free-surface particles robustly. The novel method enables background pressure to be applied at physical free surfaces and throughout the fluid, but not in non-physical voids, facilitating the suppression of such spurious voids. The KCFSE is validated for a translating square cylinder inside a rectangular numerical domain, with and without a free surface, and liquid in an oscillating rectangular tank. [ABSTRACT FROM AUTHOR]