Meshfree methods

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

Moving particle finite element method

Abstract: This paper presents the fundamental concepts behind the moving particle finite element method, which combines salient features of finite element and meshfree methods. The proposed method alleviates certain problems that plague meshfree techniques, such as essential boundary condition enforcement and the use of a separate background mesh to integrate the weak form. The method is illustrated via two-dimensional linear elastic problems. Numerical examples are provided to show the capability of the method in benchmark problems. Copyright © 2001 John Wiley & Sons, Ltd.

A natural neighbour meshless method with a 3D shell-like approach in the dynamic analysis of thin 3D structures

Abstract: This work presents the dynamic analysis of three-dimensional plate and shell structures based on an improved meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM) using a shell-like formulation. In the NNRPIM, the nodal connectivity is imposed using the natural neighbours concept. An integration background mesh is constructed, totally node-dependent, and used in the numerical integration of the NNRPIM interpolation functions, which possess the delta Kronecker property. Several dynamic plate and shell problems are studied to demonstrate the effectiveness of the method.

A Particle-Partition of Unity Method Part VII: Adaptivity

Abstract: This paper is concerned with the adaptive multilevel solution of elliptic partial differential equations using the partition of unity method. While much of the work on meshfree methods is concerned with convergence-studies, the issues of fast solution techniques for the discrete system of equations and the construction of optimal order algorithms are rarely addressed. However, the treatment of large scale real-world problems by meshfree techniques will become feasible only with the availability of fast adaptive solvers. The adaptive multilevel solver proposed in this paper is a main step toward this goal. In particular, we present an h-adaptive multilevel solver for the partition of unity method which employs a subdomain-type error indicator to control the refinement and an efficient multilevel solver within a nested iteration approach. The results of our numerical experiments in two and three space dimensions clearly show the efficiency of the proposed scheme.

Element free Galerkin approach based on the reproducing kernel particle method for solving 2D fractional Tricomi-type equation with Robin boundary condition

Abstract: The traditional element free Galerkin (EFG) approach is constructed on variational weak form that the test and trial functions are shape functions of moving least squares (MLS) approximation. In the current paper, we propose a new version of the EFG method based on the shape functions of reproducing kernel particle method (RKPM). In other words, based on the developed approach in Han and Meng (2001) the fractional Tricomi-type equation will be solved using the new technique. The fractional derivative has been introduced in the Caputos sense and is approximated by a finite difference plan of order O(3),1<<2. We use the EFG-RKPM to discrete the spatial direction. We illustrate some numerical results on non-rectangular domains. The unconditional stability and convergence of the new technique have been proved. Numerical examples display the theoretical results and the efficiency of the proposed approach. Also, the numerical results are compared with the finite element method (FEM) and EFG-MLS procedure.

An SPH model for free surface flows with moving rigid objects

Abstract: This paper presents a computational model for free surface flows interacting with moving rigid bodies. The model is based on the SPH method, which is a popular meshfree, Lagrangian particle method and can naturally treat large flow deformation and moving features without any interface/surface capture or tracking algorithm. Fluid particles are used to model the free surface flows which are governed by Navier-Stokes equations, and solid particles are used to model the dynamic movement (translation and rotation) of moving rigid objects. The interaction of the neighboring fluid and solid particles renders the fluid-solid interaction and the non-slip solid boundary conditions. The SPH method is improved with corrections on the SPH kernel and kernel gradients, enhancement of solid boundary condition, and implementation of Reynolds-averaged Navier-Stokes turbulence model. Three numerical examples including the water exit of a cylinder, the sinking of a submerged cylinder and the complicated motion of an elliptical cylinder near free surface are provided. The obtained numerical results show good agreement with results from other sources and clearly demonstrate the effectiveness of the presented meshfree particle model in modeling free surface flows with moving objects