Topic
Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
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TL;DR: In this paper, numerical solutions for flow over an airfoil and a square obstacle using Incompressible Smoothed Particle Hydrodynamics (ISPH) method with an improved solid boundary treatment approach, referred to as the Multiple Boundary Tangents (MBT) method.
121 citations
TL;DR: An adaptive procedure based on background mesh is developed for meshless methods using MLS that comprises a cell energy error estimate and a local domain refinement technique based on the Delaunay algorithm.
120 citations
TL;DR: An overview of the construction of meshfree basis functions is presented, with particular emphasis on moving least‐squares approximant, natural neighbour‐based polygonal interpolants, and entropy approximants.
Abstract: In this paper, an overview of the construction of meshfree basis functions is presented, with particular emphasis on moving least-squares approximants, natural neighbour-based polygonal interpolants, and entropy approximants. The use of information-theoretic variational principles to derive approximation schemes is a recent development. In this setting, data approximation is viewed as an inductive inference problem, with the basis functions being synonymous with a discrete probability distribution and the polynomial reproducing conditions acting as the linear constraints. The maximization (minimization) of the Shannon–Jaynes entropy functional (relative entropy functional) is used to unify the construction of globally and locally supported convex approximation schemes. A JAVA applet is used to visualize the meshfree basis functions, and comparisons and links between different meshfree approximation schemes are presented. Copyright © 2006 John Wiley & Sons, Ltd.
120 citations
TL;DR: A set of algorithms for real time computation of soft tissue deformation, starting with the finite element formulation and the integration scheme used and addressing common problems such as hourglass control and locking are presented.
119 citations
11 Jul 2014
TL;DR: A consistent meshfree Lagrangian approach for numerical analysis of incompressible flow with free surfaces, named least squares moving particle semi-implicit (LSMPS) method, is developed that can resolve the existing major issues of widely used strong-form particle method.
Abstract: In this paper, a consistent meshfree Lagrangian approach for numerical analysis of incompressible flow with free surfaces, named least squares moving particle semi-implicit (LSMPS) method, is developed. The present methodology includes arbitrary high-order accurate meshfree spatial discretization schemes, consistent time integration schemes, and generalized treatment of boundary conditions. LSMPS method can resolve the existing major issues of widely used strong-form particle method for incompressible flow—particularly, the lack of consistency condition for spatial discretization schemes, difficulty in enforcing consistent Neumann boundary conditions, and serious instability like unphysical pressure oscillation. Applications of the present proposal demonstrate remarkable enhancements of stability and accuracy.
118 citations