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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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Journal ArticleDOI
TL;DR: In this paper, the authors give an overview of issues related to the numerical simulation of adhesive spreading for liquid to semi-liquid adhesives, and the advantages and limitations are presented in order to guide the choice of the suitable approach depending on the case under consideration.
Abstract: The current work is intended to give an overview of issues related to the numerical simulation of adhesive spreading for liquid to semi-liquid adhesives. The advantages and limitations are presented in order to guide the choice of the suitable approach depending on the case under consideration. It is shown that methods are of two categories, whether they are grid-based or meshless. In the first, the movement of the matter is directly dependent on the mesh size and distribution. Contrariwise, in the meshfree methods, the particles are free to move and each carries its properties. Besides, cases of application are presented to provide a database for calculating adhesive spreading with the particulate SPH method. It is shown that it is possible to use simple behaviour laws to win this case.

3 citations

Posted Content
TL;DR: In this paper, the authors apply the polyharmonic splines (PHS) as the RBF together with appended polynomial and solve the heat conduction equation in several geometries using a collocation procedure.
Abstract: In recent years, a variety of meshless methods have been developed to solve partial differential equations in complex domains. Meshless methods discretize the partial differential equations over scattered points instead of grids. Radial basis functions (RBFs) have been popularly used as high accuracy interpolants of function values at scattered locations. In this paper, we apply the polyharmonic splines (PHS) as the RBF together with appended polynomial and solve the heat conduction equation in several geometries using a collocation procedure. We demonstrate the expected exponential convergence of the numerical solution as the degree of the appended polynomial is increased. The method holds promise to solve several different governing equations in thermal sciences.

3 citations

Proceedings ArticleDOI
26 Jul 2014
TL;DR: In this paper, a node-based method of weighted residuals (MWR) is proposed to solve the electromagnetic structure problems and a new divergence-preserved meshless method is developed as an example.
Abstract: A large number of numerical methods have been proposed and continue to be developed for solving electromagnetic structure problems. This paper presents a new look at these numerical methods and a way of unifying them with the node-based method of weighted residuals (MWR). As a result, a unifying approach to constructing of numerical methods is shown. It can then be applied to develop new numerical methods catering to specific electromagnetic issues or problems. A new divergence-preserved meshless method is developed as an example.

3 citations

Journal Article
TL;DR: In this paper, the authors compared the Finite Volumes Mixture Mixture (FVM) algorithm with the MESHLESS Mixture and the least square mixture (LSM) algorithm to solve the Navier-Stokes Equation.
Abstract: THIS STUDY COMPARES THE FINITE VOLUMES, FINITE DIFFERENCES AND MESHLESS METHODS APPLIED TO THE CLASSIC SQUARE DRIVEN CAVITY PROBLEM. IT GIVES A BRIEF EXPOSITION OF THE DRIVEN CAVITY FLOW PROBLEM, THE SCIENTIFIC MOTIVATION OF THIS STUDY, THE APPROACH EMPLOYED, AND THE GOALS TO BE ACHIEVED. THE PROJECTION METHOD WAS USED TO SOLVE THE NAVIER-STOKES EQUATIONS. A STRUCTURED MESH WAS EMPLOYED FOR THE FINITE DIFFERENCES METHOD AND AN UNSTRUCTURED MESH FOR THE FINITE VOLUMES METHOD. CELL CENTERED WAS USED FOR THE VELOCITY FIELD U AND THE PRESSURE FIELD P IN THE FINITE VOLUMES METHOD. THE CONVERGENCE WAS ACCELERATED THROUGH THE BI-CONJUGATED GRADIENT STABILIZED METHOD. THE NECESSARY POINTS TO THE MESHLESS METHOD WERE OBTAINED FROM THE COMPUTATIONAL NODES GENERATED BY THE FINITE VOLUMES MESH. THE EXPONENTIAL WEIGHT FUNCTION AND THE LEAST SQUARE METHOD WAS USED IN THE MESHLESS METHOD. THE PRIMITIVE VARIABLES WERE ADOPTED IN ALL THE FORMULATIONS AND REYNOLDS NUMBERS 0.1, 10, 50 AND 100 WERE USED. THE FORMULATIONS ARE SECOND ORDER IN SPATIAL VARIABLES AND FIRST ORDER EXPLICIT IN TIME VARIABLES. INTERESTING CHARACTERISTICS OF THE FLOW ARE PRESENTED IN DETAILS - THE VELOCITY FIELD IN THE CENTRAL LINES AND THE STREAMLINES. THE RESULTS ARE LISTED IN TABLES AND THE PRIMARY VORTEX POSITION IS COMPARED WITH OTHER AUTHORS. THE FINITE VOLUMES, MESHLESS AND FINITE DI®ERENCES METHODS ARE COMPARED AND THE ERRORS AMONG THEM ARE PRESENTED AND DISCUSSED.

3 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202355
2022112
2021102
202092
201996
201897