SPH Framework Research Articles

A SPH framework for dynamic interaction between soil and rigid body system with hybrid contact method

SummaryA smoothed particle hydrodynamics (SPH) framework for three‐dimensional dynamic soil‐multibody interaction modeling is presented, where both soils and rigid bodies are discretized using SPH particles. In the framework, soils are modeled using the Drucker‐Prager model, while rigid bodies are considered with a multibody dynamics solver. A hybrid contact method suitable for three‐dimensional simulations is developed to model the soil‐body and body‐body frictionless and frictional contacts, where contact forces are calculated based on ideal plastic collision and the unit normal/tangential vectors of the actual surface. Owing to its simplicity in contact detection and accuracy in contact force calculation, the hybrid contact method can be easily incorporated into SPH. Furthermore, graphics processing unit (GPU) parallelization is utilized to improve efficiency. The presented numerical framework and the hybrid contact method are validated using several examples. Numerical results are compared with analytical solutions and results from the literature. Furthermore, two three‐dimensional simulations involving dynamic soil‐multibody interaction are included to demonstrate the application.

Dynamic particle partitioning SPH model for high-speed fluids simulation

The popular SPH method still remains as one of the most widely-used methods in fluid simulation, exhibiting its longevity with new and diverse variants in recent decades. New progress in the SPH simulation in most recent years are still hampered by such challenge when simulating high-speed fluids. In this paper, our research efforts are devoted to the efficiency issue of the SPH simulation when the ratio of velocities among fluid particles is large. Specifically, we introduce a k-means clustering method into the SPH framework to dynamically partition fluid particles into two disjoint groups based on their velocities. Then, we use a two-scale time-step scheme for these two types of particles. The smaller time steps are for particles with higher speed in order to preserve temporal details and guarantee stability. In contrast, the larger time steps are used for particles with smaller speed to reduce the computational expense, and both types of particles are tightly coupled in the simulation. We conduct various experiments and compare our method with some of the most relevant works, which have manifested the advantages of our methods over the conventional SPH technique and its new variants in terms of efficiency and stability.

Extending Incompressible SPH framework for simulation of axisymmetric free-surface flows

Dynamics of a Newtonian fluid in a cylindrical symmetric domain can be conceptualized as axisymmetric flow. Full-scale 3D simulation of such problems requires large computational overhead. A new divergence-free Axisymmetric Incompressible Smoothed Particle Hydrodynamics (AxISPH) framework is proposed for modeling of Newtonian fluid flow with free-surface. The formulation employs the concept of variable axisymmetric volume based on current particle position to incorporate symmetry around the central axis. The framework utilizes a semi-implicit two-step approach to obtain hydrodynamic variables and minimizes errors in particle position. Laplace and gradient operators are modified to incorporate axisymmetric nature. A radial dam-break flow has been simulated with the proposed model and compared with three-dimensional ISPH result.

Mixed miscible-immiscible fluid flow modelling with incompressible SPH framework

A divergence-free Incompressible Smoothed Particle Hydrodynamics (ISPH) framework is developed for modelling multifluid immiscible/miscible flows. The numerical model considers Navier-Stokes equation along with scalar-transport equation to represent flow characteristics. Pure divergence free ISPH algorithm is used to solve Navier-Stokes momentum equation. Scalar transport equation is solved based on the nature of the fluid particles represented in terms of colour indicator (ϕ). Fixed ghost particles are utilized for simulating slip boundary. Proposed model is validated against three analytical/experimental results: (a) immiscible Rayleigh-Taylor Instability (b) lock-exchange non-Boussinesq flow (c) miscible gravity current with low density ratio. The model can capture Kelvin-Helmholtz instabilities generated at the interface. the framework is capable of capturing density-dependent flow with low to high density ratio alike. The capability of the developed model in general multifluid system is demonstrated for two cases (a) miscible multimode Rayleigh-Taylor Instability and (b) mixed miscible-immiscible fluid flow simulation.

Multiphase SPH simulation for interactive fluids and solids

This work extends existing multiphase-fluid SPH frameworks to cover solid phases, including deformable bodies and granular materials. In our extended multiphase SPH framework, the distribution and shapes of all phases, both fluids and solids, are uniformly represented by their volume fraction functions. The dynamics of the multiphase system is governed by conservation of mass and momentum within different phases. The behavior of individual phases and the interactions between them are represented by corresponding constitutive laws, which are functions of the volume fraction fields and the velocity fields. Our generalized multiphase SPH framework does not require separate equations for specific phases or tedious interface tracking. As the distribution, shape and motion of each phase is represented and resolved in the same way, the proposed approach is robust, efficient and easy to implement. Various simulation results are presented to demonstrate the capabilities of our new multiphase SPH framework, including deformable bodies, granular materials, interaction between multiple fluids and deformable solids, flow in porous media, and dissolution of deformable solids.

Mixed-mode fracture modeling with smoothed particle hydrodynamics

In this work, we describe a coupled Drucker–Prager and Grady–Kipp SPH framework in order to simulate mode I, mode II and mixed mode failure under the same formulation. This framework is then applied to study failure in uniaxial compression of gypsum samples containing a single angled flaw.To validate the model, results are compared with the experimental analysis and shows good agreement, where fracture initiation positions and angles are well represented. This trend of agreement continues beyond initiation, through to propagation, and finally post-failure behavior.The methodology and results shown here describe a powerful tool for study of fracture mechanics.

Incompressible SPH simulation of wave interaction with porous structure

In this paper an incompressible Smoothed Particle Hydrodynamics (ISPH) method is applied to investigate the flow motion in and around the porous structure. In order to describe in a simple and effective way the flow through the interface between the porous region and pure fluid region within the SPH framework, a heuristic boundary treatment method has been proposed. The ISPH model is first verified against a theoretical model of wave propagation over a porous bed and then further validated by comparing the predicted wave surface profiles and flow velocity fields with the experiment data for a typical case of flow motion around and inside a submerged porous structure. The good agreement has demonstrated that the improved ISPH model developed in this work is capable of modelling wave interaction with porous structures.

Validation of robust SPH schemes for fully compressible multiphase flows

The present study examines the ability of the SPH number-density scheme to treat multiphase problems of the fully compressible regime. The number-density scheme is extended to the fully compressible regime, using the standard variational SPH framework and incorporate artificial diffusion coming from a generic formula. Aiming at robust schemes, we adopt the differential form of mass conservation. The performance of this scheme is studied with the help of two benchmark tests. It is shown that the standard variational framework of SPH may treat multiphase processes in the fully compressible regime, without reverting to non-standard formulations. The SPH solutions are compared to solutions coming from the Arbitrary Lagrangian Eulerian method and are validated against exact solutions.

Incompressible SPH using the Divergence‐Free Condition

AbstractIn this paper, we present a novel SPH framework to simulate incompressible fluid that satisfies both the divergence‐ free condition and the density‐invariant condition. In our framework, the two conditions are applied separately. First, the divergence‐free condition is enforced when solving the momentum equation. Later, the density‐invariant condition is applied after the time integration of the particle positions. Our framework is a purely Lagrangian approach so that no auxiliary grid is required. Compared to the previous density‐invariant based SPH methods, the proposed method is more accurate due to the explicit satisfaction of the divergence‐free condition. We also propose a modified boundary particle method for handling the free‐slip condition. In addition, two simple but effective methods are proposed to reduce the particle clumping artifact induced by the density‐invariant condition.

Implementation of Smoothed Particle Hydrodynamics for Detonation of Explosive with Application to Rock Fragmentation

The paper presents a methodology in the SPH framework to analyze physical phenomena those occur in detonation process of an explosive. It mainly investigates the dynamic failure mechanism in surrounding brittle rock media under blast-induced stress wave and expansion of high pressure product gases. A program burn model is implemented along with JWL equation of state to simulate the reaction zone in between unreacted explosive and product gas. Numerical examples of detonation of one- and two-dimensional explosive slab have been carried out to investigate the effect of reaction zone in detonation process and outward dispersion of gaseous product. The results are compared with those obtained from existing solutions. A procedure is also developed in SPH framework to apply continuity conditions between gas and rock interface boundaries. The modified Grady–Kipp damage model for the onset of tensile yielding and Drucker–Prager model for shear failure are implemented for elasto-plastic analysis of rock medium. The results show that high compressive stress causes high crack density in the vicinity of blast hole. The major principal stress (tensile) is responsible for forming radial cracks from the blast hole. Spalling zones are also developed due to stress waves reflected from the free surfaces.

SPH procedures for modeling multiple intersecting discontinuities in geomaterial

SummaryA methodology is developed in SPH framework to analyze the behavior of preexisting multiple intersecting discontinuities or joints in rock material. The procedure does not require any additional unknowns to represent discontinuities and to capture velocity jump across them. Instead, a discontinuity is represented by a set of joint particles placed along the discontinuity plane, in which relative velocity and traction vector is evaluated, obeying the Mohr–Coulomb friction law with zero tension constrain. For failure of continuous rock material, the Drucker–Prager yield criterion with tensile cracking is employed in the elastic‐plastic constitutive model. Free‐sip, no‐slip, and symmetric boundary conditions are also implemented in SPH framework for proper representation of physical system.The paper analyzes behavior of a rock sample having a discontinuity plane under uniaxial loading and compares velocity and stress with a theoretical solution derived considering effective vertical stiffness of the joint planes. The efficacy of the proposed method is successfully demonstrated by solving another two problems of jointed rock mass under uniaxial and gravitational loading conditions.Copyright © 2014 John Wiley & Sons, Ltd.

Modeling accidental-type fluid–structure interaction problems with the SPH method

This paper presents the validation aspects of a unified numerical framework based on SPH formulation and devoted to the modeling of fluid–structure interaction problems involving large motion of the fluid and large deformation with a possible failure of the structure. The fluid domain is modeled according to an updated Lagrangian formulation. The solid domain (3D and shell models) uses the total Lagrangian formulation. The fluid–structure interaction is treated via a unilateral contact algorithm adapted to SPH context. The SPH framework is verified on academic test cases and validated by simulating an experiment involving the reservoir leakage.

Hydrodynamical Simulations of Narrow Planetary Rings. I. Scaling

We investigate the global dynamics of the uranian rings using a modified 2-D smoothed particle hydrodynamic code combined with a 2-D tree code used to compute the particle-to-particle gravitational interactions. This code includes epicyclic fluid motion, nonaxisymmetric flow, local and nonlocal shear viscosity, self-consistent scale height evolution, ring–satellite gravitational interaction and coevolution, and ring self-gravity. To follow the scale height of each SPH particle we solve the vertical momentum equation for the flow using a Runge-Kutta scheme with a second order polynomial fit to the vertical behavior of the fluid pressure (N. Borderies et al., 1985, Icarus63, 406–420). The behavior of the fluid viscosity is obtained from I. Mosqueira (1996, Ph.D. thesis, Cornell University, Ithaca, NY), who found good agreement between a low optical depth extension of the high optical depth nonlocal viscosity model of Borderies et al. (1985) with the results of a local patch-code ring simulation. Our present viscosity model includes a further correction which accounts for the epicyclic limit to the mean free path (P. Goldreich and S. Tremaine, 1978, Icarus34, 227–239). This treatment covers both the high and the low ring density regimes so long as the fluid treatment remains valid. All energy source and sink terms in the presence of a nonzero fluid velocity divergence are self-consistently considered, including terms not considered in prior studies of rings. Furthermore, a new method has been tested and used to remove the noise contribution to the viscous momentum flux which occurs in traditional treatments of the viscosity within the SPH framework. In the present context this correction is needed to assure a physical behavior for the ring. Even within a 2-D framework the uranian rings are so narrow compared to their semimajor axes that radial resolution requires too many particles given our present computer resources. To address this issue we have developed a physical scaling that reduces the semimajor axis of the ring while preserving its width and, we believe, retains the relevant global satellite–ring dynamics. In the case of ring resolution on the order of kilometers, with a value of the scaling parameter that reduces the ring's semimajor axis by a factor of 20, our scaling allows for savings between a factor of 500 in the case of synodic time scales to a factor of 10,000 for viscous time scales. We expect this scaling to figure significantly in numerical studies of the global dynamics of planetary rings in the future. In the present study we use this scaling to follow the evolution of an epsilon-like ring in the presence of an m=2 mode (but no satellites) with and without self-gravity. In these runs, chosen as an initial demonstration of the usefulness and applicability of our scaling, the ring can be seen to evolve in the presence of shear.