The smoothed finite element methods (S-FEM) are a family of methods formulated through carefully designed combinations of the standard FEM and some of the techniques from the meshfree methods. Studies have proven that S-FEM models behave softer than the FEM counterparts using the same mesh structure, often produce more accurate solutions, higher convergence rates, and much less sensitivity to mesh distortion. They work well with triangular or tetrahedral mesh that can be automatically generated, and hence are ideal for automated computations and adaptive analyses. Some S-FEM models can also produce upper bound solution for force driving problems, which is an excellent unique complementary feature to FEM. Because of these attractive properties, S-FEM has been applied to numerous problems in the disciplines of material mechanics, biomechanics, fracture mechanics, plates and shells, dynamics, acoustics, heat transfer and fluid–structure interactions. This paper reviews the developments and applications of the S-FEM in the past ten years. We hope this review can shed light on further theoretical development of S-FEM and more complex practical applications in future.

Smoothed Finite Element Methods (S-FEM): An Overview and Recent Developments

Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)

Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications

In ocean engineering, the applications are usually related to a free surface which brings so many interesting physical phenomena (e.g. water waves, impacts, splashing jets, etc.). To model these complex free surface flows is a tough and challenging task for most computational fluid dynamics (CFD) solvers which work in the Eulerian framework. As a Lagrangian and meshless method, smoothed particle hydrodynamics (SPH) offers a convenient tracking for different complex boundaries and a straightforward satisfaction for different boundary conditions. Therefore SPH is robust in modeling complex hydrodynamic problems characterized by free surface boundaries, multiphase interfaces or material discontinuities. Along with the rapid development of the SPH theory, related numerical techniques and high-performance computing technologies, SPH has not only attracted much attention in the academic community, but also gradually gained wide applications in industrial circles. This paper is dedicated to a review of the recent developments of SPH method and its typical applications in fluid-structure interactions in ocean engineering. Different numerical techniques for improving numerical accuracy, satisfying different boundary conditions, improving computational efficiency, suppressing pressure fluctuations and preventing the tensile instability, etc., are introduced. In the numerical results, various typical fluid-structure interaction problems or multiphase problems in ocean engineering are described, modeled and validated. The prospective developments of SPH in ocean engineering are also discussed.

Smoothed particle hydrodynamics and its applications in fluid-structure interactions

Meshless Local Petrov--Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity

Two-phase flow involves complex interface evolution process such as the formation, development, pulsation, and rupture of phase interfaces. Numerical simulation is one of the important means to study two-phase flow. The tracking and reconstruction of phase interface is the focus of two-phase flow simulation. A two-phase flow simulation algorithm based on coupled incompressible smoothed particle hydrodynamics (ISPH) method and finite volume method (FVM) is developed in this article. In present ISPH-FVM coupling algorithm, one phase which has smaller volume is represented by SPH particles, while the other phase is defined on the FVM grids. The coupling of ISPH and FVM is achieved through the transfer and interaction of physical parameters at the overlapping area of the SPH particles and FVM grids. The continuous medium surface force model is also introduced into the ISPH-FVM coupling algorithm to study the effect of surface tension on the two-phase flow. Several numerical examples of two-phase flow are adopted to verify the effectiveness of the ISPH-FVM coupling method. 

An
 ISPH‐FVM
 coupling algorithm for interface tracking of two‐phase fluid flows

A sub-domain radial point interpolation method is proposed to simulate problem of linear elasticity. In present method, the problem domain is firstly divided into sub-domains with arbitrary shape, and then, nodes without connectivity are imbedded in every sub-domain. The local variational weak formulation is established over sub-domains, in which nodes within the sub-domain are used for approximation. Local discrete equations of weak form are simplified by condensation of degree of freedom, which transfers equations of inner nodes to equations of boundary nodes based on sub-domains. Compatibility of displacement in adjacent sub-domains and convergence of present method are discussed. And displacements and its gradient are continuous in the entire problem domain. In contrast to an early formulation of RPIM based on Galerkin weak form, which is proposed by Liu and coworkers, certain modifications are presented to increase its computational efficiency in this paper. Numerical examples show that computational efficiency of present method is higher than that of standard RPIM based on Galerkin weak form, and good accuracy, high convergence can also be obtained.

A sub-domain RPIM with condensation of degree of freedom

Two‐phase flow involves complex interface evolution process such as the formation, development, pulsation, and rupture of phase interfaces. Numerical simulation is one of the important means to study two‐phase flow. The tracking and reconstruction of phase interface is the focus of two‐phase flow simulation. A two‐phase flow simulation algorithm based on coupled incompressible smoothed particle hydrodynamics (ISPH) method and finite volume method (FVM) is developed in this article. In present ISPH‐FVM coupling algorithm, one phase which has smaller volume is represented by SPH particles, while the other phase is defined on the FVM grids. The coupling of ISPH and FVM is achieved through the transfer and interaction of physical parameters at the overlapping area of the SPH particles and FVM grids. The continuous medium surface force model is also introduced into the ISPH‐FVM coupling algorithm to study the effect of surface tension on the two‐phase flow. Several numerical examples of two‐phase flow are adopted to verify the effectiveness of the ISPH‐FVM coupling method.

An incompressible smoothed particle hydrodynamics‐finite volume method coupling algorithm for interface tracking of two‐phase fluid flows

Purpose – The purpose of this paper is to study the ability of SPH method in simulating shock initiation process. The initiation and subsequent explosion processes of condensed explosive involve high-pressure propagation and material large deformation, which increase the simulation difficulty in using traditional mesh-based method. The study aims to take the SPH method as an alternative method to shock initiation simulation. Design/methodology/approach – The SPH method combined with some correct aspects is applied to simulate the shock initiation process. The condensed explosive is ignited by the impact of high-speed flyer. In order to avoid the non-physical penetration between particles of high-velocity flyer and condensed explosive, a particle to particle contact algorithm is employed. After the ignition, the detonation process of condensed explosive is represented by the ignition and growth model. A modified SPH method based on Riemann-solver is applied to smooth the numerical oscillation at shock fron...

Simulation of one dimension shock initiation of condensed explosive by SPH method

Reinforced composite materials are widely used in industry and also have attracted the interest in academia due to their superior properties. The numerical methods are usually employed for evaluating the microscopic mechanical properties of composite materials. In this paper, an efficient numerical approach is developed by coupling the strain smoothing technique and the rebar element technique base on the framework of traditional finite element method. The proposed approach can be applied with the simple meshes, and it requires few degrees of freedom compared to the traditional finite element method, thus the computational time and storage requirement are significantly reduced. In addition, the quality of solutions with the distorted meshes can also be assured, and the coordinate mapping and the calculation of Jacobian matrix can be eliminated. On the other hand, the local strain/stress is captured by reanalysis with substructure technique. The superior performances of the proposed approach are numerically demonstrated with several numerical examples compared with the traditional finite element method, especially the distorted meshes can also yield reasonable results. Finally, the proposed approach is employed for the evaluation of the equivalent elastic properties of polymeric nano-composites material, which reaffirms that the present approach has good performance.

Dean Hu

Papers

An ISPH‐FVM coupling algorithm for interface tracking of two‐phase fluid flows

A sub-domain RPIM with condensation of degree of freedom

An incompressible smoothed particle hydrodynamics‐finite volume method coupling algorithm for interface tracking of two‐phase fluid flows

Simulation of one dimension shock initiation of condensed explosive by SPH method

Evaluation of equivalent material properties of reinforced composites by a novel smoothed rebar element technique