Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.

Techniques for boundary conditions in point allocation meshless methods

Abstract: Because of amazing advantages of meshless numerical methods over classical finite difference methods and finite element methods,the point allocation method and its characteristics are introduced. Several techniques for derivative boundary conditions by meshless allocation method are summarized and a new technique based on integral interpolation is proposed. Using meshless allocation method based on point interpolation to solve Helmholtz problem,the superiority of the proposed technique is verified.

Semi-implicit operator splitting for the simulation of Herschel-Bulkley flows with smoothed particle hydrodynamics

Abstract: Smoothed particle hydrodynamics (SPH) has become a popular numerical framework of choice for simulating free-surface flows, mainly for Newtonian fluids. The topic regarding the simulation of non-Newtonian free-surface flows, however, remains relatively untouched due to difficulties regarding the computation of viscous forces. In previous approaches, the viscous forces acting on each SPH particle were computed explicitly. Non-Newtonian fluids such as Herschel–Bulkley fluids, the effective viscosity between yielded and unyielded regions can differ by several orders of magnitudes; imposing severe time step restrictions for the simulation for explicit methods. Numerically, this can be seen as a stiff problem. We propose a semi-implicit time-stepping approach where the viscous forces are computed implicitly, within the context of SPH. We demonstrate the convergence of the method via a simple 2D test case.

Comparing Several Different Numerical Approaches for Large Deformation Modeling with Application in Soil Dynamic Compaction

Abstract: Abstract Dynamic compaction (DC) is vastly utilized to improve the strength characteristics of the soils. To predict the soil deformations derived from the DC operations, usually numerical simulation analysis is applied. For the conduction of such simulations, several numerical approaches with different elemental formulations can be used. From the perspective of finite element analysis (FEA), there are four main formulations including the Lagrangian, Arbitrary Lagrangian-Eulerian (ALE), Coupled Lagrangian-Eulerian (CEL), and Smoothed Particle Hydrodynamic (SPH). In this research, a comparative study has been conducted to evaluate the computational efficiency of those four approaches in the prediction of soil large deformations during the DC operations. To do this, for a DC operation executed in a road embankment construction project in China, the real field data was compared to the results obtained from the numerical simulations via the ABAQUS program. The findings demonstrate that of all those approaches, the Lagrangian approach delivers the minimum accuracy of the predicted results, albeit with the least running time. In contrast, the ALE formulation predicted closer estimations of soil deformations although it was found to be less time-efficient. Interestingly, the CEL and SPH approaches predicted the soil deformations with the maximum degree of accuracy whereas they were not as time-efficient as the Lagrangian approach. To address this issue, a hybrid model of Lagrangian and SPH formulations was constituted to satisfy the maximum accuracy with the minimum running time. Such a hybrid model is highly applicable for the accurate prediction of soil large deformations during the DC operations.

Updated Lagrangian Taylor-SPH method for elastic dynamic problems

Abstract: This paper presents a discussion on the properties of the collocation meshfree method, the Updated Lagrangian Taylor-SPH (UL-TSPH), for dynamic problems in solid mechanics. The PDEs are written in mixed form in terms of stress and velocity for the elastodynamics problems. Two sets of particles are used to discretize the partial differential equations, resulting on avoiding the tensile instability inherent to classical SPH formulations. Numerical examples ranging from propagation of a shock wave in an elastic bar to a stationary Mode-I semi-Infinite cracked plate subjected to uniaxial tension are used to assess the performance of the proposed method.