Comparison of MPS and SPH methods for solving forced motion ship flooding problems

Comparison investigations of numerical simulations of incompressible viscous flows by the SPH (smoothed particle hydrodynamics) and the MPS (moving particle semi-implicit) are presented. A dam-break problem is chosen as the test case. In the calculation with the SPH method, weakly compressible model is used, i.e. WCSPH, which describes water as a nearly incompressible fluid, while in MPS method, the pressure Poisson equation is introduced to keep the density of fluid to be constant. The numerical results show that the two particle methods are robust and flexible, numerical results qualitatively agree with the experimental data. It can be seen that both the SPH method and the MPS method can be easily applied to the complex free surface flow problems.

The stress intensity factors or strain energy release rate are typically used to characterise the stress field in the vicinity of a crack in fracture mechanics. One way to obtain the strain energy release rate in elastic–plastic fracture mechanics is from the stress and deformation field around the crack tip through the calculation of the J integral. The J-integral is contour independent, although the contour must start and end from a traction-free surface, such as the crack surface. Using Green’s theorem, the J-integral can be formulated as a surface or area integral, which makes it convenient for implementation in finite element method (FEM). More importantly, the J-integral calculation is insensitive to uncertainty of the exact crack tip location, can be applied for linear elastic analysis with small scale yielding and in an improved formulation for elastic plastic fracture. In short, the J-integral is an indispensable tool in the study of fracture mechanics. Despite the J-integral being widely used in FEM, including availability in most commercial FEM codes, there is currently no algorithm to calculate the J-integral in the Smoothed Particle Hydrodynamics (SPH) method. This is somewhat surprising since the SPH method, due to its meshless nature, has inherent advantages in dealing with cracks compared to mesh based methods such as FEM. In this paper we will therefore address this deficiency and develop an algorithm for calculation of the J integral in the SPH method. The implementation of his new alghorithm is based on a new definition of the weighting function q 1 , as appropriately normalised kernel function, which inherently satisfies all the specific requirements on q 1 : The function is sufficiently smooth in the J-integral area, it is equal to unit inside contour path of the integral and zero outside of the path. A further element of novelty is that in the current implementation, the gradient of this function is evaluated analytically rather than through a numerical approximation. The verification and validation of developed algorithm is based on simulation of the standard single edge notch tension test (SENT) under the plain strain conditions. The SPH results are compared to the FEM results for stress and displacement fields in the vicinity of the crack tip, as well as the J integral solutions. The SPH results demonstrated convergence and were within 2% of the converged FEM solutions. The validation also allows for the definition of simple guidelines for the definition of the J-integral area to achieve accurate results. The implementation is currently developed for linear elastic fracture mechanics applications, but its generalisation and application to elastic plastic fracture mechanics, including the combination with elastic plastic constitutive models is straightforward. • New algorithm to calculate J-Integral developed in Smoothed Particle Hydrodynamics (SPH). • New approach for calculating gradient of J-Integral weighting function q 1 analytically. • Confirmed accuracy of J-integral results from SPH compared to FEM results.

This paper presents some of our results in using of the Smoothed Particles Hydrodynamics (SPH) method for the numerical modelling of the detonation phenomena. The study of the detonation is very important for evaluation of different explosives and even for their design. The paper also presents, in a synthetically way, some fundamentals of the detonation. The numerical modelling of the detonation can be made by Finite Element Method (FEM), but using of the SPH method brings some important advantages because the large deformations, large distortions occur. If the FEM can be used in Arbitrary Lagrangian-Eulerian (ALE) formulation, the SPH method can easily works and next to it, some specific parameters (density variation, specific energy etc.) can be obtained and analyzed by post-processing. The numerical results (by FEM and by SPH method) are compared with theoretical results. The numerical study allowed us to analyse the influence of some explosive characteristics and of the circumstances (non confined and confined explosive) upon detonation parameters.

The smoothed particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) are well-known and efficient mesh-less numerical methods widely used to investigate a wide range of complicated practical engineering problems. Recently, two modified Laplacian models [1, 2] have been proposed by using different efficient mathematical techniques, and the analogy between SPH and MPS methods. These two models exhibit significantly superior precision in comparison with several existing modified schemes [3-9] but still suffer from lower accuracy near calculation domain boundaries as they work with the conventional weight or interpolation functions. In this paper, the models were reformulated and further improved by replacing the weight functions with well-known moving least squares (MLS) shape functions without requiring dummy calculation nodes beyond boundaries. The proposed Laplacian models in this study could achieve very accurate results compared with the existing models [1, 2] for the solution of four different two-dimensional Poisson equations on irregular node distributions.

Numerical simulations of water wave dynamics based on SPH methods

Application of the Lagrangian meshfree approach to modelling of batch crystallisation: Part I—Modelling of stirred tank hydrodynamics

In this paper, a new bird model which combined the visco-elastic material properties and Smooth Particle Hydrodynamics (SPH) method has been proposed to simulate the bird features in high-speed conditions. A rigid plate impact test was adopted to compare the reaction of SPH and Lagrangian bird model. Compared with the results of Lagrangian bird model, new SPH model was more in line with the experimental data, and has better computational efficiency. The SPH bird model was further used to bird impacting with the wing leading edge by using finite element program LS-DYNA. Two kinds of leading edge structural enhancement programs have been proposed and carried out simulation of bird impact. Basis of calculation, the design parameters of experimental structure was determined and was produced to wait for final testing.

An improved Riemann SPH-Hamiltonian SPH coupled solver for hydroelastic fluid-structure interactions

Many numerical methods have been proposed in the efforts to revel the failure mechanism of the brittle materials, such as rock and concrete, under various loading conditions. It is of continuous interests on properly modeling the heterogeneous microstructure and to account for its effects on the macroscopic material failure; and effectively tackling the initial and created discontinuities, such as fractures and fragmentations in the failure process. In this thesis, a numerical approach based on the mesh-free Smoothed Particle Hydrodynamics (SPH) method is developed that is able to simulate the dynamic failure of brittle materials by capturing the detailed occurring sequence of the microscopic cracks as well as the macro mechanical response. An elasto-plastic damage model based on the extension of the Unified Strength Theory is adopted in order to better reflect the strength behavior of the materials. To model the material heterogeneity, a statistical approach has been utilized. In addition, a polymineral model for the multi-phased materials has been incorporated to simulate heterogeneous materials with different compositions more appropritely. A series of numerical simulations in 2-D and 3-D on rock-like material failures are performed using the developed program. The influences of material heterogeneity as well as the strain rate on the material fracture process and its dynamic strength are investigated and compared with experimental results. Comparisons show that they agree well qualitatively. Particularly, the results reveal that the strain rate dependency of the dynamic tensile and compressive strength might be ascribed to the apparent confining pressure effects by the rapid loading. It shows that the developed program is very promising in conducting such kind of simulations and deserves further improvements for many other applications.

Liquefaction can result in the damage or collapse of structures during an earthquake and can therefore be a great threat to life and property. Many site investigations of liquefaction disasters are needed to study the large-scale deformation and flow mechanisms of liquefied soils that can be used for performance assessments and infrastructure improvement. To overcome the disadvantages of traditional flow analysis methods for liquefied soils, a soil–water-coupled smoothed particle hydrodynamics (SPH) modeling method was developed to analyze flow in liquefied soils. In the proposed SPH method, water and soil were simulated as different layers, while permeability, porosity, and interaction forces could be combined to model water-saturated porous media. A simple shear test was simulated using the SPH method with an elastic model to verify its application to solid phase materials. Subsequently, the applicability of the proposed SPH modeling method to the simulation of interaction forces between water and soil was verified by a falling-head permeability test. The coupled SPH method produced good simulations for both the simple shear and falling-head permeability tests. Using a fit-for-purpose experimental apparatus, a physical flow model test of liquefied sand has been designed and conducted. To complement the physical test, a numerical simulation has been undertaken based on the soil–water-coupled SPH method. The numerical results correspond well with the physical model test results in observed configurations and velocity vectors. An embankment failure in northern Sweden was selected so that the application of the soil–water-coupled SPH method could be extended to an actual example of liquefaction. The coupled SPH method simulated the embankment failure with the site investigation well. They have also estimated horizontal displacements and velocities, which can be used to greatly improve the seismic safety of structures.

The boundary layer between an accretion disk and the surface of a compact object is simulated using the Smoothed Particle Hydrodynamics (SPH) method. The equations include radiation, which is treated in the flux limited diffusion approximation. The integrated equations and some numerical simulations of the 31) motion of the gas are presented.

This paper discusses alternative Lagrangian formulations for smooth particle hydrodynamics method. These Lagrangian formulations are here employed in solving large strain problems that involve elasto-plastic and hyperelastic materials. It has previously been shown in the literature that the Lagrangian formulation for continuum eliminates the problem of tension instability which is generally coupled with Eulerian continuum formulation of smooth particle hydrodynamics and other meshless methods. This paper presents the details of the methodologies used in formulating Lagrangian smooth particle hydrodynamics method and their characteristics.

Ultrasonic-assisted grinding, a promising processing technique for machining hard and brittle materials, is already quite extensively employed in manufacturing industries. However, the material removal mechanism in ultrasonic-assisted grinding is not yet fully understood, which hinders its further application. This study investigates the material removal process in ultrasonic-assisted scratching (UAS) of SiC ceramics using both simulation and experiment method, in order to detail the material removal mechanism in ultrasonic-assisted grinding. A conventional scratching (CS) test was also carried out, but without ultrasonic vibration for comparison. The simulated workpiece is modeled by smooth particle hydrodynamic (SPH) particles. Results show the following: (1) the SPH method is suitable to investigate the material removal mechanism during ultrasonic-assisted grinding of hard and brittle materials. (2) The profile of scratching trace in ultrasonic vibration (UV) is a sinusoidal path. UV vibrating in the direction vertical to the workpiece results in material removed in either a continuous or a discontinuous mode. UV vibrating in the direction parallel to the workpiece expands the cutting area. (3) The groove depth in UAS is much bigger than that in CS. (4) UV results in the impact of the abrasive grain on the workpiece, causing the deformation field to spread from the impact site and leading to deeper scratching depths and larger radial and lateral cracks.

Numerical wave flume with improved smoothed particle hydrodynamics

A smooth particle hydrodynamic (SPH) method combined with the Herschel–Bulkley-Papanastasiou (HBP) model is proposed to simulate 3D concrete printing (3DCP). HBP model can better resolve the divergence of equivalent viscosity coefficient under small deformation and extend the compatibility of simulation to dilatant and pseudoplastic fluids, so it possesses natural superiority in modelling the 3D printing of cement-based material with visco-plastic rheology behaviour. The HBP-based SPH method considers the influence of the printing parameters including nozzle characteristics and printing-to-extrusion velocity ratio on the cross-sectional geometry of the deposited filament, and its outcomes agree qualitatively well with the experiment results. Furthermore, by utilising process parameters furnished by simulation cases, it is possible to determine the critical conditions under which filaments printed by different nozzle shapes are vulnerable to tearing, and the corresponding critical intervals when tearing occurs are also defined. 3DPC experiments verify these findings and confirm that SPH simulation provides additional information on the geometric characteristics of single-layer structures, as well as physical quantities that cannot be straightforwardly measured.