Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling

Abstract

This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. As a mesh-free Lagrangian method suitable for complex flows with interfaces and multiple phases, SPH has developed considerably in the past decade. While original applications were in astrophysics, early engineering applications showed the versatility and robustness of the method without emphasis on accuracy and convergence. The early method was of weakly compressible form resulting in noisy pressures due to spurious pressure waves. This was effectively removed in the incompressible (divergence-free) form which followed; since then the weakly compressible form has been advanced, reducing pressure noise. Now numerical convergence studies are standard. While the method is computationally demanding on conventional processors, it is well suited to parallel processing on massively parallel computing and graphics processing units. Applications are diverse and encompass wave–structure interaction, geophysical flows due to landslides, nuclear sludge flows, welding, gearbox flows and many others. In the state of the art, convergence is typically between the first- and second-order theoretical limits. Recent advances are improving convergence to fourth order (and higher) and these will also be outlined. This can be necessary to resolve multi-scale aspects of turbulent flow.

Modified dynamic boundary conditions (mDBC) for general-purpose smoothed particle hydrodynamics (SPH): application to tank sloshing, dam break and fish pass problems

“…If the matrix is ill-conditioned, the boundary particle is given the Shephard filtered ghost node density found in Eq. (11). The boundary particles have zero velocity as before.…”

“…The meshless nature of SPH and the issue of kernel truncation near boundaries can create difficulties in enforcing solid boundary conditions, and, accordingly, boundary conditions have been highlighted as one of the Grand Challenges of SPH [10]. A recent review addressing accuracy in SPH is provided by Lind et al [11], and a review of applications in coastal and ocean engineering is available in Gotoh and Khayyar [12] Many different approaches have been proposed in the literature to enforce solid boundary conditions, and they can be grouped into three main types: the first approach is the method of repulsive forces ( [13,14]), which enables the discretization of 2-D and 3-D irregular geometries. However, non-physical forces are added to prevent particle penetration and kernel truncation is not addressed and so the accuracy of SPH spatial interpolation near the walls is remarkably reduced.…”

Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction

“…Nevertheless, the SPH Research and Engineering International Community (SPHERIC), https://spheric-sph.org, accessed on 5 April 2021, has identified a series of Grand Challenges [16] that need to be overcome to further extend the usage of SPH in industrial applications. In particular, the present work addresses the first of these Grand Challenges which is the low accuracy and convergence rate of the method [6]. Indeed, the theoretical second order spatial accuracy of the continuous SPH integral interpolation [17] cannot be achieved with the original SPH formulation [3] and usually the convergence rate practically attained is around first order.…”

“…Since then, SPH has been used in a large number of applications that range from environmental and coastal engineering to energy production [4]. Nowadays, SPH is widely used for Computational Fluid Dynamics [5,6] and applied to a number of problems in hydraulics, including wastewater works [7], turbine design [8], fish passage flows [9], interaction of free-surface flows with flexible structures [10], sloshing in partially filled tanks [11], analysis of Wave Energy Converters (WEC) [12], study of the impact of sea waves on structures [13], and Large Eddy Simulation (LES) modelling of turbulent flows for moderate [14] and, more recently, high [15] Reynolds numbers. For geometrically complex problems and/or multiphysics applications for which the creation of computational grids is a practical burden, SPH already represents a real alternative to more established mesh-based tools.…”

Numerical modeling of fluid-structure interaction (FSI): time-consistent pressure computation, rigid bodies contact and coupled particle-mesh methods.

“…for fluid and solid modeling, we have smoothed particle hydrodynamics (SPH) method (Gingold & Monaghan, 1977;Lucy, 1977), and moving particle semi-implicit (MPS) method (Koshizuka & Oka, 1996). Nowadays, there are innumerous variations of these two methods (Li et al, 2020;Lind et al, 2020). Besides the difference between the discrete operators Based on contact mechanics theories, the objective of this work is to propose a solid-solid contact model for the particle-based methods, especially for the MPS method, by adopting a nonlinear spring and dashpot model for solid-solid contact, similar to that adopted by Canelas et al (2016), but with newly defined normal direction and distance of contact vectors to improve the numerical stability, and therefore reproducing the macroscopic properties of the multiple bodies interactions in transient incompressible flows involving free surface and impulsive hydrodynamic loads.…”