A novel meshfree approach based on the finite pointset method for linear elasticity problems

Saucedo-Zendejo, Félix R.

doi:10.1016/j.enganabound.2021.12.011

Cited by 5 publications

(2 citation statements)

References 44 publications

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“…This work has been used by many authors to create point clouds for meshfree simulations [119,122,124,155,170,194], and has been generalized to different ends [79]. While the original work required a surface mesh, it has been generalized for different boundary specifications [43,79].…”

Section: Meshfree Advancing Front Methodsmentioning

confidence: 99%

Point Cloud Generation for Meshfree Methods: An Overview

Suchde

Jacquemin

Davydov

2022

Arch Computat Methods Eng

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Meshfree methods are becoming an increasingly popular alternative to mesh-based methods of numerical simulation. The biggest stated advantage of meshfree methods is the avoidance of generating a mesh on the computational domain. However, even today a surprisingly large amount of meshfree literature ironically uses the nodes of a mesh as the point set that discretizes the domain. On the other hand, already existing efficient meshfree methods to generate point clouds are apparently not very well known among meshfree communities, which has led to recent work redeveloping existing algorithms. In this paper, we present a brief overview of point cloud generation methods for domains and surfaces and discuss their features and challenges, in particular in the context of applicability to industry-relevant complex geometries.

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Section: Meshfree Advancing Front Methodsmentioning

confidence: 99%

Point Cloud Generation for Meshfree Methods: An Overview

Suchde

Jacquemin

Davydov

2022

Arch Computat Methods Eng

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“…We use a Generalized Finite Difference Method (GFDM) approach to compute numerical derivatives. The GFDM is a strong form meshfree collocation approach that has been widely used [14,35,67,69], and shown to be a robust framework for a variety of flow applications [38,64] including flow through porous media [47], non-Newtonian flow [50,66], and even for soil mechanics [37], and elasticity problems [49]. The GFDM approach used here is second order accurate, with polynomial basis functions.…”

Section: Numerical Schemementioning

confidence: 99%

Volume and Mass Conservation in Lagrangian Meshfree Methods

Suchde¹,

Leithäuser²,

Kuhnert³

et al. 2023

Preprint

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Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: unreliable volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing especially in meshfree collocation methods. Using these, we introduce an artificial compression or expansion in the fluid to rectify errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour, even for complex industrial test cases such as automotive water crossing.

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